The Royal Wolverhampton NHS Trust confirmed the building was temporarily closed as a "precautionary measure" after two members of non-clinical staff tested positive for the virus.
But they added that all patient services remain operating as normal – with no changes to phone or video appointments.
Any patient who requires a face-to-face appointment will be seen at another site, the trust confirmed.
A message had gone out to all patients explaining that Penn Manor Medical Centre building has been closed temporarily. A sign had also been pinned on the door of the surgery – thanking patients for understanding during "a very difficult period".
In a message to patients, bosses said: "Penn Manor Medical Centre building is currently closed due to shielding of all staff.
"Please use the email firstname.lastname@example.org for all queries, appointments and prescription requests, this email will be manned all day by staff at Coalway Road and Warstones Surgeries.
"For anything that you consider a medical emergency please call Coalway Road surgery on 01902 339296 and they will endeavour to help guide you to one of our clinical team.
"Our GPs and ANPs are still working. If you struggle to get through or need to be seen face to face more urgently please attend the walk in services at the Urgent Care Centre at New Cross or Phoenix Centre.
"Thank you for your kind consideration during this difficult period."
A spokesman for the Royal Wolverhampton NHS Trust said: "Penn Manor Medical Centre building is temporarily closed as a precautionary measure due to two members of non-clinical staff testing positive for Covid-19.
"However all patient services remain operating as normal, with no changes to phone or video appointments.
"Patients who require face-to-face appointments will be seen at another site. They can also email email@example.com for more information.
"The building will reopen following a deep clean."
"The safety of our patients and colleagues is of upmost importance to us and we have therefore sought specialist advice and guidance from experts in Public Health. They advise us that the risk to service users is low."