Vaccination is increasingly a requirement to be hired, as employers ranging from accounting and software firms to schools and restaurants are asking applicants to be inoculated against Covid-19.

The share of job postings stating that a new hire must be vaccinated have nearly doubled in the past month, according to the job search site Indeed. The total number remains low, roughly 1,200 postings requiring a vaccination per million in the first week of August. But that is well up from about 600 in early July, and about 50 per million job postings in early February.

Many of the postings don’t explicitly name Covid-19 as the vaccine required for employment, said Indeed economist AnnElizabeth Konkel, who wrote the report, but broader context of the job descriptions suggested most employers were referring to the coronavirus vaccine, as opposed to other shots. Early this year, before Covid-19 vaccines were widely available in the U.S., very few job postings outside of healthcare positions indicated a vaccination requirement, she said.

“While the number of postings requiring a vaccine is still low, it’s a trend that’s really taking off,” Ms. Konkel said. “I think a growing number of employers are trying to keep workers safe and do not want to shut down again this winter....They see vaccines as the way out of this pandemic.”

The increased number of job postings requiring vaccination comes at a time when the number of coronavirus cases is surging because of the fast-spreading Delta variant. Employers ranging form the federal government and state of California to McDonald’s Corp. and Walt Disney Co. are saying that at least some of their workers must soon be vaccinated against Covid-19 to report to worksites, or in some cases face frequent testing or other requirements.

The share of job postings, per million, in the education sector that required a vaccination rose to 2,166 in July from 33 in February, according to Indeed. In food service, the rate per million rose to 814 in July from 43 in February. The rate per million for accounting rose to 1,184 from 39, and in software development the rate increased to 438 from four.

The postings are advertisements intended to attract applicants and don’t necessarily reflect the company’s policy toward existing workers. Some postings simply state “vaccine required,” while others give more specific details or offer alternatives, such as frequent testing and mask wearing.

Ms. Konkel said there is no evidence in Indeed data that job searchers are looking specifically for positions that require or don’t require vaccinations. She said some job postings mention that the existing staff have been vaccinated or that the company is offering a small bonus to workers willing to be vaccinated.

Low-wage work is in high demand, and employers are now competing for applicants, offering incentives ranging from sign-on bonuses to free food. But with many still unemployed, are these offers working? Photo: Bloomberg The Wall Street Journal Interactive Edition

Participation in the labor force fell during the pandemic, when some would-be job seekers had concerns about interacting with the public or had heightened family-care responsibilities, and others chose to retire. But Jonathan Meer, a labor economist at Texas A&M University, said he doesn’t think vaccine requirements will have a significant impact on the number of adults willing to take jobs.

There were more than 10 million unfilled jobs at the end of June, a record on data back to 2000, and more than the number of unemployed job seekers, according to the Labor Department. And many employers say they can’t find enough workers to fill positions.

“The labor market is tight enough that there will likely be employers who are willing to overlook vaccination status,” he said.

Nearly 30% of adults in the U.S. haven't received at least one dose of a Covid-19 vaccine, according to the Centers for Disease Control and Prevention. The shots are widely available at no cost to recipients. According to the Kaiser Family Foundation, 14% of respondents to a July survey said they would “definitely not” be vaccinated against Covid-19.

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Steven Jenkins, 37 years old, is among those who say they won’t be vaccinated. The Fort Collins, Colo., resident said he was fired two months ago from a security job he recently started after he refused to wear a mask and subsequently engaged in an argument over the matter with his boss.

Mr. Jenkins, who remains unemployed, said he won’t take a job that requires him to be vaccinated or wear a mask. He said he has natural immunity from the virus because he’s recovered from a Covid-19 infection and that it is his right to not be vaccinated over concerns about the shot’s long-term effects.

“The job market doesn’t look too good for me because I won’t wear a mask, and more companies here in Colorado are requiring it,” he said. “We live in a sissy culture. Do you get wet if I don’t have an umbrella? Why do you care if I’m not vaccinated, if you are?”

Doctors and public-health officials have said unvaccinated people are far more likely to contract Covid-19 and face more severe outcomes than those who are vaccinated, but given the highly contagious nature of the Delta variant, even some fully vaccinated people exposed to the virus are at risk of breakthrough infections.

Many large employers are requiring vaccines for current employees.

McDonald’s Corp. said Wednesday that all of the company’s U.S. corporate employees, but not restaurant workers, must be fully vaccinated by Sept. 27. “A resurgence of infections caused by Covid-19 variants has many of us uneasy,” McDonald’s Global Chief People Officer Heidi Capozzi said in the message to U.S. employees. “We’ve heard from many of you that you would feel more comfortable returning to the office if you had more certainty your colleagues were vaccinated.”

United Airlines and Tyson Foods Inc. are among the companies requiring all employees to be vaccinated. Others, such as Walmart Inc., have said white-collar workers must be vaccinated. Last month President Biden said federal workers, including those in the military, would be required to receive a vaccine or face testing.

Labor unions are somewhat split on vaccine requirements. The union that represents United’s pilots and the largest federal workers union have said such a policy should be negotiated in collective bargaining, but the Association of Flight Attendants-CWA and American Federation of Teachers are encouraging members to get vaccinated.

Other employers such as General Electric Co., Caterpillar Inc. and Snap-on Inc. have said they won’t require workers to get shots. U.S. employers can require that all workers physically present in a workplace be vaccinated against Covid-19, the Equal Employment Opportunity Commission said earlier this year.

Michael Farren, an economist at George Mason University’s right-leaning Mercatus Center, said if workers see their refusal to become vaccinated as a threat to their career, they could change their views. He added that vaccine verification systems are weak, and that those who refuse to take the shot may lie or forge documentation to remain employed.

“Some employers will require vaccines to limit the potential for production disruptions, or to cater to customers’ desires,” he said. “In the same way, some employers will not require vaccines as a way of indulging their own social preferences, or to cater to customers with those social preferences.”

—Heather Haddon contributed to this article.

Write to Eric Morath at eric.morath@wsj.com