The Food and Drug Administration is expected next week to grant full approval of the Covid-19 vaccine from Pfizer Inc. and partner BioNTech SE, according to people familiar with the planning, an action that could spur more vaccination requirements by employers and encourage more people who are hesitant to get vaccinated.

The two-dose shot was first cleared in December by the agency on an emergency use basis for people 16 years and older. The emergency designation allows for products to be distributed during public-health crises based on the best available evidence.

Opponents of mandatory vaccinations have cited the emergency approval as grounds for not requiring inoculations, so full approval is expected to lead more businesses and institutions to require mandatory vaccinations.

Public health officials and vaccine experts also hope full approval will sway some people who have been hesitant to get vaccinated. About 60% of eligible people in the U.S. are fully vaccinated, according to federal figures.

Three in 10 unvaccinated adults said they would be more likely to get vaccinated if one of the vaccines currently authorized for emergency use were to receive full approval from the FDA, according to a June poll by the Kaiser Family Foundation.

The agency had been under pressure by some public health leaders who said the FDA was moving too slowly to grant approval during a pandemic where unvaccinated people are more likely to develop severe infection.

Pfizer asked for full approval in early May. The agency is working rapidly and hopes to have something to announce by the middle of next week, one of the people familiar with the planning said. The timing was reported earlier by Politico.

Of the three authorized vaccines in the U.S., only Pfizer has submitted all the required information to the FDA, according to the companies, and analysts expect it to be the first receive clearance.

Moderna Inc., whose authorized two-dose shot uses similar mRNA technology as the Pfizer-BioNTech, has said it is still completing rolling data submissions. Johnson & Johnson, whose shot was authorized in February, has said it plans to file for full approval later this year.

Pfizer and BioNTech won emergency approval from the FDA last year by showing their vaccine was 95% effective in preventing symptomatic disease after two months. The vaccine bested the agency’s standard that Covid-19 vaccines be at least 50% effective at preventing disease in a placebo-controlled trial to receive an emergency-use authorization, the same bar that must be cleared for full approval.

Pfizer and BioNTech have said their approval application includes longer-term clinical trial data from more than 46,000 volunteers that showed the vaccine was 91.3% effective up to six months after the second of two doses. The emergency-use authorization issued last year was based on data from about 38,000 volunteers who were followed for a median of two months after the second dose.

Once fully approved, the vaccine would be eligible for off-label prescriptions, such as booster doses, according to the FDA. However, analysts said, the critical element for broad boosting is a recommendation from the Advisory Committee on Immunization Practices to the FDA, as physicians often follow ACIP recommendations.

With full approval, Pfizer would likely be permitted to market the vaccine to doctors, providers and the general public as it does with other approved products. The FDA is permitted to restrict such communications with emergency authorization.

Vaccination requirements have been accelerating in the U.S. despite some public resistance and efforts by states such as Arkansas to ban vaccine mandates. Some laws prohibiting vaccination mandates are tied only to vaccinations that have emergency use authorization, so they may not apply once Pfizer gets FDA approval.

Some employers such as Walmart Inc. and Uber are requiring some employees to be vaccinated unless they have approved exceptions.

Write to Stephanie Armour at stephanie.armour@wsj.com and Jared S. Hopkins at jared.hopkins@wsj.com