The pandemic has unleashed a historic burst in entrepreneurship and self-employment. Hundreds of thousands of Americans are striking out on their own as consultants, retailers and small-business owners.

The move helps explain the ongoing shake-up in the world of work, with more people looking for flexibility, anxious about covid exposure, upset about vaccine mandates or simply disenchanted with pre-pandemic office life. It is also aggravating labor shortages in some industries and adding pressure on companies to revamp their employment policies.

The number of unincorporated self-employed workers has risen by 500,000 since the start of the pandemic, Labor Department data show, to 9.44 million. That is the highest total since the financial-crisis year 2008, except for this summer. The total amounts to an increase of 6% in the self-employed, while the overall U.S. employment total remains nearly 3% lower than before the pandemic.

Entrepreneurs applied for federal tax-identification numbers to register 4.54 million new businesses from January through October this year, up 56% from the same period of 2019, Census Bureau data show. That was the largest number on records that date back to 2004. Two-thirds were for businesses that aren’t expected to hire employees.

This year, the share of U.S. workers who work for a company with at least 1,000 employees has fallen for the first time since 2004, Labor Department data show. Meanwhile, the percentage of U.S. workers who are self-employed has risen to the highest in 11 years. In October, they represented 5.9% of U.S. workers, versus 5.4% in February 2020.

The self-employment increase coincides with complaints by many U.S. companies of difficulties—in some cases extreme—in finding and retaining enough employees. In September, U.S. workers resigned from a record 4.4 million jobs, Labor Department data show.

Kimberly Friddle, 50 years old, quit her job as head of marketing for a regional mortgage company near Dallas in September 2020. Her daughters in the sixth and eighth grade were struggling with attending school virtually, and, months into the pandemic, both were showing signs of anxiety. Although her employer was understanding, she wanted flexibility to provide them help without juggling Zoom meetings and projects.

Ms. Friddle planned to stay home indefinitely with the support of her husband, a pharmaceutical-company executive. But when a friend contacted her the next month, she saw an opportunity.

The friend sold home décor items on Amazon.com from his home in Canada, and Covid-related border restrictions were making it difficult to process returns. When he explained what he needed—primarily, someone to examine returned items for damage and ship them back to Amazon—Ms. Friddle felt the work could be a good challenge and a chance for her older daughter, Samantha, to gain some work experience.

They began processing returns for him steadily. When other Amazon sellers he knew needed help with warehouse-related tasks that were also made harder by the pandemic, he referred them to Ms. Friddle.

Now she runs an Amazon logistics, warehousing and fulfillment business full time from the family’s home outside Houston and rented warehouse space nearby. Her older daughter works with her about 10 hours a week, and Ms. Friddle recently hired an assistant. She hopes to expand her services to Walmart vendors.

In July, the family’s monthly income returned to roughly what it was when she worked in marketing, Ms. Friddle said. Though the decision to leave that job was an emotional one, she said, a change after 27 years has given her new energy and confidence in addition to the flexibility.

“I didn’t have a plan when I left,” she said. “I wasn’t giving enough attention to the needs of my family. I wasn’t giving enough attention to the job that needed to be done. I felt like I was failing everywhere.”

Now, “I feel so successful and I wake up every day like, ‘I wonder what’s going to happen today.’ ”

Through the late 19th century, the majority of Americans worked for themselves, as farmers or artisans. With new technology such as electric lighting, manufacturing expanded, and many people left the field for the factory floor. They landed in an environment of strictly defined work hours and hierarchies—workers overseen by managers overseen by executives.

By the time Covid-19 arrived in the U.S., the advent of apps, websites and companies catering to entrepreneurs and freelancers was already giving employees options.

Then, the pandemic spurred some people to “pause and re-evaluate their priorities,” said Aaron De Smet, a McKinsey & Co. senior partner and consultant on labor trends. “When you have a big event where everybody takes stock, and trends are already in place, people working for an employer never thought of doing freelance but now when [they] think about it, why not?”

Marcus Grimm, a 50-year-old in Lancaster, Pa., worked at advertising agencies from the time he finished college. For years, he toyed with freelancing. “I had always considered it, but literally just never had the guts to make the move,” he said. “I was scared I would lose sleep every night worrying about my next dollar.”

Early in the pandemic, Mr. Grimm, a married father of two grown children, was laid off. He logged onto Upwork, a website that connects freelance workers from a wide range of industries with potential clients. He fielded several assignments doing ad campaigns for big companies, charging a low hourly rate.

Business flowed in. He has steadily raised his rate, to $150 an hour. Mr. Grimm said he now earns more than in his old job, which paid $130,000 a year.

His favorite part is not having to deal with corporate politics or any bureaucracy. He can go kayaking in the middle of the day.

“I’m the one who finds the client, I’m the one who does the work, and I’m the one who deals with any of the problems that come up,” he said.

One client offered to hire him full-time, but he declined, Mr. Grimm said. “I told them, ‘I’ve seen the light.’”

Etsy Inc., an online marketplace for individuals to buy and sell items, says it had 7.5 million active sellers as of Sept. 30—up 2.6 million from that time in 2019. Eight in 10 are women. Its surveys indicate more than 4 in 10 of the new sellers started their businesses for reasons related to the pandemic, including for some the need to stay home to care for family members.

On a recent investor call, Upwork Inc. Chief Executive Hayden Brown, citing a September 2020 survey, said: “A new type of career path has emerged, with half of the Gen Z [age 18 to 22] talent pool actually choosing to start their careers in freelance rather than full-time employment.”

Based on a summer 2021 survey, Upwork concluded that 20% of people working remotely during the pandemic were considering leaving their jobs for freelance work.

At LinkedIn, the number of members who indicate they are self-employed by listing services from a field called “Open to Business” has quadrupled since the pandemic began, to 2.2 million, the company said. Nearly half of the new entrepreneurs have a college degree and nearly 4 in 10 a postgraduate degree.

Enterprises founded by women have grown by 27% and male-founded ones by 17% since the pandemic started, according to a LinkedIn analysis of user profiles. Meanwhile, Labor Department data show that in the two years through July, the number of self-employed female workers actively at work has grown 4.3%, while the number of self-employed male workers is down 1%, according to a Pew Research analysis.

Limited child-care or commuting options have helped spur some of the moves.

Matt Parrish of Raleigh, N.C., worked for a company that built retaining walls since graduating from the University of Florida roughly a decade ago. An engineer who managed projects, Mr. Parrish, 31, grew tired of dealing with the bureaucracy, such as when he wanted to hire someone.

“I enjoyed the work I was doing, but I definitely felt like I was getting more and more pigeonholed because it was such a large company,” he said.

He also wanted a schedule allowing more time with his newborn daughter. His employer provided just two weeks of paid parental leave, he said.

Mr. Parrish resigned in August and went into business as a consultant to homeowners and commercial-building owners on building retaining walls for construction projects. Being able to work from home and care for his daughter throughout the day was a primary reason, he said.

Instagram, YouTube and TikTok have provided new avenues to raise cash for aspiring entrepreneurs. Meanwhile, Robinhood Markets Inc. and cryptocurrencies such as bitcoin have spurred a new generation of traders, some so successful they have quit their jobs to trade.

Josh Dorgan, who is 32, started trading cryptocurrencies in 2017 with a straightforward goal: to pay off the mortgage on a house he and his wife had bought in Omaha, Neb., as fast as possible.

Mr. Dorgan continued working as a pediatric nurse while trading litecoin, ether and XRP. His trading, plus advisory roles he took on with crypto companies, started taking more time, hard to balance with his job managing the dialysis unit at Children’s Hospital & Medical Center in Omaha.

When he told his wife, also a nurse, he wanted to quit and focus just on investing, she insisted they talk to a financial adviser first. With a professional’s signoff, he quit the hospital job in August 2020. He said his trading profits the following week equaled his previous full-year salary.

He tries to confine his work—including advising digital-currency firms and creating content for his nearly 200,000 Twitter followers—to between 8:30 a.m. and noon, leaving time to spend with his 10-month-old son, golfing and visiting a lake house he and his wife bought recently.

“You don’t just get into the markets and make money out of thin air,” said Mr. Dorgan. Yet even in volatile trading conditions, he said, he feels far less pressure than when he was juggling investing with a full-time job: “When I’m at a red light, I don’t feel like I’m rushed to get home anymore.”

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Part of the current shift to self-employment might prove temporary. The boom in self-employed day traders during the dot-com hoopla of the late 1990s deflated along with the stock bubble.

A sharp rise in savings—boosted by a federal supplement to unemployment benefits, most recently $300 a week, that was paid for as long as 18 months of the pandemic—provides some individuals a financial cushion to pursue self-employment. As they run down those savings, some might again want a regular paycheck, economists say.

In addition, if labor shortages ease, freelancers could face stiffer competition from companies in landing clients. Finally, if the pandemic recedes, so might one piece of the impetus to leave regular work in favor of self-employment. Five percent of unvaccinated adults say they left a job because of a vaccine requirement they opposed, according to a Kaiser Family Foundation survey in October.

Robert Spencer, 55, repaired bridges for Washington state’s government for nearly a decade as a welder and fabricator. Mr. Spencer, who had a bout of Covid-19 early in the pandemic, left the job in October because he wasn’t willing to comply with a vaccine mandate for state employees.

As his end-date approached, Mr. Spencer, who had worked for himself before joining the state, began buying supplies to run his own fencing business and lining up residential projects.

His wife now handles billing and accounts payable and receivable. He says the two will need to make financial adjustments in anticipation of a winter slowdown in home improvement.

If the state should change its rules and let everybody come back, “then obviously I would, because of the benefits,” Mr. Spencer said. “But until then—I’m not counting on it—I plan on doing what I’m doing now. I enjoy it.”