Part of the Cape Hill store was opened as a vaccination centre last month, with the aim of delivering 240 jabs per day.
Now Sandwell Council has revealed 11 Covid cases within the store, but Asda said none of them were among staff working on the vaccines.
The council said it was not consulted when the vaccine centre was set up and has reported its concerns.
A Sandwell Council spokesman said: "Since being notified of this situation, we have contacted the store and given detailed public health advice on managing the spread of infection.
"Our environmental health officers have also visited the store. We expect the store to act appropriately under the Health & Safety at Work regulations and fully comply with our advice.
"We continue to do all we can to warn people about the risks of picking up the virus.
"Supermarkets have been highlighted as potential high risk locations and we wrote to all those in our area recently to remind them of their responsibilities.
"The setting up of vaccination centres in pharmacies is controlled by NHS England. The local authority was not consulted on this occasion. However, we have sent our report on the cases in Asda to NHS England.
"The council has reported its concerns over the location of this centre."
Asda transformed the George clothing department at the store to accommodate the vaccination centre, operating from 8am to 8pm.
A spokesman for Asda said there are "stringent clinical regulations" in place for the hub as well as separate relaxation area for colleagues working in the vaccine centre.
He added: “We are proud to host a vaccine centre at our Cape Hill store, which was identified as a safe and appropriate location by NHS England as part of their work to establish vaccination sites throughout the local area.
"The vaccination hub is separated from our main store, is operated by dedicated colleagues and is subject to enhanced, infection prevention control and Covid security measures. It provides a safe and convenient location for members of the local community to access the vital Covid-19 vaccine.
“Whilst we do not comment on individuals, we can absolutely assure our customers that our Cape Hill store follows strict Covid safety measures for both customers and colleagues.
"This includes the enforcement of mask wearing and social distancing, the provision of masks and sanitising stations and Covid Marshals operating in stores. We work collaboratively and proactively with the local authority, who were happy with the measures in place in our store during their most recent visit.”
Sandwell Council’s director of public health, Dr Lisa McNally, thanked Asda for its prompt response in September last year after eight workers at its Cape Hill store tested positive for Covid-19.
Efforts to encourage customers to wear face coverings were stepped up, including the provision of single-use masks at the entrance to the store.