Lime Tree Court care home, in Coseley, closed to visitors on Wednesday and all staff are remaining on site alongside residents.
The facility, which cares for about 50 elderly people some of which have dementia, has shut after receiving expert medical advice.
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A spokesperson for Sanctuary Care, which runs the care home, said: "The safety of our residents and staff is our priority and in line with the expert medical advice we have received, we can confirm that Lime Tree Court is currently in a period where everyone is remaining on site and no visitors are allowed.
"Our staff have volunteered to remain at the home and we are hugely grateful for their commitment to providing high quality care.
"We are in regular contact with the Department of Health and Social Care and other care providers to share information and best practice, and can reassure the families of all our residents and staff that we are closely following the detailed public health guidance being given to care homes right across the country."