The centre, believed to be the first to open inside a supermarket in England, will operate at an Asda branch in Birmingham from the week starting on January 25.
The retailer has been selected by NHS England to operate the centre from its in-store pharmacy, with qualified staff administering the vaccine to priority groups identified by the NHS.
The centre, believed to be in Small Heath, will operate from 8am to 8pm, seven days a week, and have the capacity to administer 250 jabs per day. It will clear space from its George section in order to create the room needed.
Asda bosses said the site is the first Asda pharmacy to be approved to support the Pfizer/BioNTech vaccine programme, and the chain is continuing to work with Public Health England and NHS England to assess other sites across the country.
The firm said in a statement: "Individuals in priority groups will receive their appointment from the NHS and have the option to select the Asda store as a convenient location to receive their vaccination. They should not contact the store directly.
"Asda has also offered NHS England the full use of its 238 in-store pharmacies and qualified pharmacists to support the rollout of the Oxford/AstraZeneca vaccine programme which has just begun.
"As this variant of the vaccine is easier to transport and store, it could be administered from Asda's full network of in-store pharmacies throughout the country."
Roger Burnley, Asda CEO and president, said: "We are incredibly proud to provide this service and are keen to do all we can to help the NHS and Government accelerate the rollout of the vaccination programme.
"We have an extensive nationwide logistics network that could support the storage and distribution of the vaccine and our highly-trained pharmacy colleagues are experienced in delivering large vaccination programmes, having recently provided nearly 200,000 flu jabs to members of the public.
"We are on hand to provide the NHS with any practical support required so that more people can quickly receive the vaccine."
The move by Asda comes as the Government attempts to ramp up vaccinations in order to reach its target of protecting two million people each week, with vulnerable people getting their jabs by mid-February and all adults by autumn.
Millennium Point in Birmingham was this week set up as one of seven mass testing centres across the country. They are being added to by other centres in the next days and weeks, including one at the Black Country Museum, which is expected to open next week. Community and sports centres are also being takemover as well as GP surgeries and pharmacies. And teams are going out into the community to reach care homes and older people in their own homes.