The facility at the Phoenix Health Centre on Parkfield Road was closed on Wednesday and yesterday.
The nature of the building repairs is not yet known.
People are being advised to call NHS 111 or go to the urgent treatment centre at New Cross Hospital if they need urgent care.
The Royal Wolverhampton NHS Trust tweeted yesterday: "Due to unforeseen emergency building repairs at the Phoenix Health Centre, the Urgent Treatment Centre is currently closed. If you need urgent care please call NHS 111 or alternatively you can attend the UTC at New Cross Hospital, which is located above the emergency department."
The account posted an update later in the day which said: "Unfortunately the Urgent Treatment Centre will remain closed tomorrow.
"If you need urgent care, you can call NHS 111 or attend the UTC at New Cross Hospital, this is located above the emergency department."