Eight workers at the Asda branch in Cape Hill, Smethwick, tested positive for the virus on Monday, with all of the staff now self-isolating.
Although the supermarket stayed open, the pharmacy department was sealed off yesterdayfor a deep clean and is back open today.
Health chiefs said a "number of people" who tested positive in the borough over the last two weeks had visited the store.
But they said there was no evidence of any link between them becoming infected and the supermarket despite cases continuing to rise.
Latest infection rates in region:
The list is based on Public Health England data published on September 1 on the Government’s coronavirus online dashboard.
Data for the most recent three days (August 30-September 1) has been excluded as it is incomplete and likely to be revised.
From left to right, the list reads: name of local authority; rate of new cases in the seven days to August 29; number (in brackets) of new cases recorded in the seven days to August 29; rate of new cases in the seven days to August 22; number (in brackets) of new cases recorded in the seven days to August 22.
Birmingham 29.4 (336), 24.3 (278)
Sandwell 27.7 (91), 21.0 (69)
Wolverhampton 12.5 (33), 16.7 (44)
Walsall 8.8 (25), 14.0 (40)
Dudley 8.4 (27), 6.5 (21)
Wyre Forest 7.9 (8), 4.9 (5)
Shropshire 7.7 (25), 7.1 (23)
Stafford 5.1 (7), 5.1 (7)
Telford and Wrekin 3.3 (6), 11.7 (21)
South Staffordshire 1.8 (2), 5.3 (6)
Cannock Chase 1.0 (1), 7.9 (8)
A total of 91 people tested positive in Sandwell in the seven days to Saturday, compared to 69 people the week before, according to Public Health England,
The latest data shows the borough had an infection rate of 27.7 cases per 100,000 people that week, an increase from 21 cases the week before.
This is more than double the rate of infection in Wolverhampton, which had the second highest rate of the four Black Country boroughs at 12.5 cases per 100,000 people.
However the rate in Birmingham remained even higher at 29.4 cases per 100,000 people.
An urgent incident management team meeting was held about the outbreak yesterday with bosses from Asda, Public Health England and the council attending.
Dr Lisa McNally, Sandwell Council's director of public health said: "We are grateful to Asda for their ongoing cooperation in this situation. They have good infection control policies in place and responded quickly to this recent outbreak.
"All businesses need to be especially careful to maintain social distancing on their premises and ensure face coverings are worn.
"I need to remind people that Covid-19 illness can be fatal and we continue to be very concerned by the very high infection rates in Smethwick."
More Covid-19 coverage:
Dr James Chipwete, consultant in communicable disease control with PHE Midlands, urged people to remain vigilant over coronavirus.
He said: "We know that Smethwick is an area where we have an increased rate of Covid-19, so it is vital that people observe social distancing and wear face coverings in enclosed public places, including when going shopping."
"The law clearly states that only people with actual medical exemption and children under 11 years old are permitted to go without face coverings in enclosed public places."
A spokesperson from Asda said: “We have been working collaboratively with Public Health England and Sandwell Council and they are satisfied with the steps we are taking to ensure that our store is a safe place to shop.
"All of the affected areas have undergone an extensive deep clean and the colleagues who tested positive self-isolated immediately."