The Wall Heath Tavern updated customers on their Facebook page after a member of the pub's team tested positive for the virus.
Several other staff were told to self-isolate and have since tested positive.
Bosses at the pub say they will now be closed until further notice – and will update their social media pages when they can reopen.
The pub is one of several in the Black Country which have temporarily closed in recent weeks as infection rates increase across the region.
More Covid-19 coverage:
A statement posted on Facebook said: "Unfortunately after one of our back of house team tested positive for Covid-19, we sent several staff away to isolate.
"Today [Thursday], we can confirm they have tested positive, meaning yet another couple members of staff will have to be tested and sent into isolation.
"The team members that have tested positive have not been in close contact with any of our customers and so no risk is present to customers that have visited us recently.
"We feel we need to take extra precautions to ensure everyone's safety at our pub. We will be closed until further notice.
"This allows time for all staff members to isolate and lessen the risk of further spreading. This is a huge financial loss – however, public safety is at the forefront of this decision."
Earlier this week three other pubs in the Dudley borough - The Rose and Crown in Brierley Hill, The Fellows in Dudley and The Red Lion in Amblecote - also announced closures due to positive tests.