The Ashmore Inn in Ashmore Park, Wolverhampton, sent out a message on its Facebook page to let customers know about the closure.
The positive test came from a customer who had visited the pub on Griffiths Drive on Saturday, September 19 and Sunday, September 20.
The Hawthorns Leisure pub will be deep cleaned during the closure and all staff are having Covid-19 tests.
A spokesman said: "We have been informed that one of our customers who visited the Ashmore on September 19 has tested positive for Covid-19.
"The Ashmore is now closed temporarily as we deep clean the pub and all team members receive results from their Covid-19 test.
"Anyone who is affected will be contacted by NHS Track and Trace and we look forward to reopening and welcoming customers back when it is safe to do so."
To find out more information about the Ashmore and when it will reopen, go to facebook.com/theashma/