Tyson Foods Inc.’s decision Tuesday to require Covid-19 vaccinations for its entire U.S. workforce drew pushback from some union leaders, signaling tensions between management and workers over stepped-up efforts to guard against the disease.

The Arkansas-based company’s target, which includes both processing plant and corporate office workers, is partly subject to discussions with labor unions that represent around one-third of the company’s hourly workers, Tyson officials said.

The company said it would offer a $200 bonus to its front-line workers as an incentive, though some union leaders pushed back, saying U.S. regulators hadn’t yet fully approved the vaccines.

Chief Executive Donnie King said the effort is the best way to protect the health of Tyson’s 120,000-person U.S. workforce as more contagious variants of Covid-19 drive infections higher across the country.

“We did not take this decision lightly,” Mr. King wrote in a memo to employees. “We have spent months encouraging our team members to get vaccinated—today, under half of our team members are.”

The move by Tyson, the biggest U.S. meat supplier by sales, comes as some of the nation’s biggest companies tighten vaccination and mask policies in response to rising Covid-19 infections. Morgan Stanley has required employees to be vaccinated before they return to the bank’s offices, and last week Google and Facebook Inc. said they would require all employees at their U.S. campuses to be vaccinated.

Meatpacking workers were among the hardest hit as infections began to spread in the U.S. in spring 2020, with tens of thousands of plant workers infected and more than 130 deaths, according to labor union estimates.

Tyson, as well as other major meat companies including JBS USA Holdings Inc. and Smithfield Foods Inc., since the beginning of 2021 have hosted vaccination events and in some cases offered incentives such as cash or free meat for employees to get vaccinated. So far, meat companies haven’t mandated vaccinations, instead mounting educational campaigns, at times in conjunction with worker groups.

The United Food and Commercial Workers International Union, which represents about 24,000 Tyson meat plant workers in the U.S. and has supported voluntary vaccine efforts, said Tyson’s mandate needs negotiating with worker representatives. The Food and Drug Administration should provide full approval of Covid-19 vaccines to address lingering questions among workers, the union said.

“UFCW will be meeting with Tyson in the coming weeks to discuss this vaccine mandate and to ensure that the rights of these workers are protected, and this policy is fairly implemented,” said Marc Perrone, the union’s president.

Tyson has started discussions on the requirement with labor unions representing its workers, a spokesman said. The FDA has authorized Covid-19 vaccines for emergency use, and Pfizer Inc. and Moderna Inc. have sought full approval. FDA officials have said the agency is working as quickly as possible.

Magaly Licolli, co-founder of the worker-advocacy group Venceremos, said mandating vaccinations would help protect more Tyson employees and alleviate some workers’ fears that unvaccinated colleagues could pose an infection risk. Ms. Licolli’s group, which works with Arkansas chicken-plant employees, had previously said meat plants shouldn’t mandate vaccines for workers.

In Arkansas, Ms. Licolli said, about 35% of the state’s population is fully vaccinated. “These companies now have the responsibility to push that forward,” she said.

Some meat-processing workers have been reluctant to take the vaccines. Concerns over safety and effectiveness have deterred some, along with language barriers, worker advocates have said. While labor unions representing meat plant workers have joined with meat companies to promote vaccination, union officials have said the shots shouldn’t be required.

While Covid-19 vaccinations are highly effective at preventing hospitalizations or death from the virus, they’re not foolproof in preventing infection. This poses problems for events like the Olympics and raises broader questions about immunity in the long term. Photo: David Crigger/Bristol Herald Courier/Associated Press The Wall Street Journal Interactive Edition

JBS, a major beef and pork processor, is requiring vaccination of new hires for its corporate offices, a trial program the company began a few months ago. JBS is monitoring reaction from potential applicants, but it is still too early to draw any conclusions, a spokesman said.

Tyson said about 56,000 of its U.S. workforce have been vaccinated, and coronavirus infection rates among its employees remain low. As infections rise across the country, Mr. King wrote, “it is abundantly clear that getting vaccinated is the single most effective thing we can do to protect ourselves, our families and our communities.”

Stuart Appelbaum, president of the Retail Wholesale and Department Store Union, which represents workers in poultry-processing plants run by JBS and Tyson, as well as in other food companies such as General Mills Inc. and Kraft Heinz Co. , said many of its members are concerned about getting the vaccine. Those concerns include worries about potential effects on individual health and distrust of government, along with skepticism over the pandemic itself due to politicization of the virus, Mr. Appelbaum said.

“Our focus has been on encouraging workers to get vaccinated by providing them with real information and negotiating with employers to make getting vaccines easier,” he said.

To vaccinate tens of thousands of meat cutters, maintenance workers and other employees across hundreds of processing plants, Tyson plans to hold more on-site vaccination events and will direct some employees toward local health departments or pharmacies. Tyson’s poultry operations are spread across the South, with roughly one-fifth of its U.S. workforce in Arkansas alone, and thousands more workers staff beef, pork and prepared foods plants in Iowa, Nebraska, Kansas and other Midwestern states.

Tyson plans for all company officers and executives to be vaccinated by Sept. 24, and all office workers by Oct. 1. All other employees are expected to be vaccinated by Nov. 1, though workers represented by labor unions will be subject to bargaining on the matter, Tyson said.

New Tyson hires must be fully vaccinated before they start work. Tyson said exceptions will be made on religious or medical grounds. Once fully vaccinated, front-line workers will be paid $200, Tyson said.

Tyson estimated it has spent about $700 million related to the pandemic, including purchasing masks and automated temperature scanners.

—Jesse Newman contributed to this article.

Write to Jacob Bunge at jacob.bunge@wsj.com