Skowhegan, Maine—Pat and John Thomas were watching the news one night last week when they saw that Walmart in this central Maine town of 8,000 people was taking appointments for the Covid-19 vaccination. They had signed up for shots at a hospital about a month ago but still hadn’t heard back. Ms. Thomas, a 74-year-old retiree, jumped on the computer.

On Friday the couple got the Skowhegan Walmart’s first doses under a new federal government program that provides Covid-19 vaccines directly to retail pharmacies across the country.

“We’ll be able to see our family and friends,” said Ms. Thomas, a former assistant manager at a bank who has been married to her husband, a 78-year-old retired accountant, for 48 years. “It will just be nice to be able to visit and go somewhere when you’re not afraid.”

Walmart Inc., the U.S.’s largest retailer and private employer, is set to become one of the biggest distributors of the Covid-19 vaccine as the federal government enlists retail pharmacies to accelerate what has been a choppy rollout.