Tyson Foods Inc. said it secured labor unions’ support for its Covid-19 vaccine mandate, with the company agreeing to a new paid sick leave policy for plant workers.

The company said the agreement with the United Food and Commercial Workers International Union and the Retail Wholesale and Department Store Union, which together represent about 80% of Tyson’s unionized employees, would keep workers safe and help Tyson’s recruitment efforts. Since announcing the vaccination requirement for its 120,000 U.S. workers on Aug. 3, Tyson said more than 30,000 have been vaccinated.

The Arkansas company estimated that about three-quarters of its U.S. workforce now have received at least one dose of a Covid-19 vaccine.

Tyson, the biggest U.S. meat company by sales, moved to require Covid-19 vaccinations for its entire U.S. workforce after company and union efforts to promote the shots had resulted in under half of those employees being inoculated since the shots became widely available early this year. The UFCW said the mandate needed to be negotiated with labor leaders and that full approval by the U.S. Food and Drug Administration would help ease some workers’ concerns about the vaccines’ safety. About 31,000 Tyson workers in the U.S. are unionized, the company said.

The FDA on Aug. 23 granted full approval to the vaccine developed by Pfizer Inc. and BioNTech SE. Tyson will provide exemptions for some workers on a medical or religious basis, the UFCW said.

While Covid-19 vaccine mandates for rank-and-file workers so far remain relatively rare across corporate America, labor unions have in some cases supported employers’ efforts. Walt Disney Co. in late August reached a deal with unions representing workers at Disney World in Florida that will require around 40,000 workers to be fully vaccinated by Oct. 22, and union leaders representing AT&T Inc. workers have been negotiating with that company to make sure its mandate was implemented fairly, union officials have said.

U.S. employers have broadly encouraged workers to get vaccinated against Covid-19, offering incentives and time off for workers who take the shots, though some companies have stopped short of mandating vaccinations for fear of losing workers in a tight labor market. Other companies, like Walmart Inc., have focused vaccine requirements on managers and corporate workers, versus hourly employees.

Tyson’s policy announced Friday will provide up to 20 hours of paid sick leave a year for fully vaccinated workers, beginning in 2022, which the UFCW called the first policy of its kind for a major meatpacking company. Tyson also will give new hires one week of paid vacation after six months of employment, Tyson said. The new policies cover all of Tyson’s U.S. facilities, and will apply to union and nonunion employees.

Workers in the U.S. meat industry were among the hardest hit during Covid-19’s initial spread through the country in spring 2020. The UFCW estimated that 132 meatpacking workers died from Covid-19. Spreading infections led to temporary shutdowns of some of the country’s biggest meat plants, and companies installed automated temperature checks and issued face coverings to workers.

While companies including Tyson have said infections among workers have fallen, meat processors this year are grappling with labor shortages that have constrained production of chicken wings, bacon and other products as the U.S. economy reopens. In August, Tyson executives said that on any given day at least 10% of positions in the company’s plants are unstaffed, and that it takes Tyson six days to get five days’ worth of normal production from its operations.

Tyson last month reported a 42% increase in quarterly profits, boosted by demand from reopening restaurants.

The Biden administration announced that Americans who have been fully vaccinated with a two-dose regimen against Covid-19 should receive a booster, citing the threat from the highly contagious Delta variant. WSJ breaks down what you need to know. Photo: Hannah Beier/Reuters The Wall Street Journal Interactive Edition

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