Part of the George clothing department has been given over to the vaccination clinic which will be overseen by Asda's in-store pharmacy team.
Patients will be invited by the NHS to book vaccination appointments at Asda. It will not be possible to book directly with the supermarket.
The new clinic is part of a national initiative by Asda which has already set up similar centres in Birmingham and Watford. Earlier this month the supermarket chain said it had administered 10,000 jabs in just five weeks.
The Asda Old Kent Road store will join a growing network of vaccination centres in SE1, including Guy's Hospital and St Thomas' Hospital. Local GP practices in north Southwark are also offering jabs at the Artesian Health Centre in Bermondsey.
The St George's Pharmacy at the Elephant & Castle has also been approved by NHS England to provide COVID-19 vaccinations.