The Downsman in Wakehurst Drive, Crawley, said the tests were taken as a precaution despite staff showing ‘little to no signs of symptoms’.
A spokesman for the pub added: “[They] have not been on the premises since early last week and are now self isolating.
“We have been in contact with Public Health England to make them aware of the situation and as a result we have chosen to close briefly to carry out a further deep clean of the pub as a precaution for the safety of our customers.
“We have followed all of the required steps at this stage and the details of customers who have visited us have been made available to the NHS Test and Trace team.”
The pub hopes to reopen very soon once it has been assured it is safe to do so, he added.
The spokesman said: “Thank you all for your understanding at this time and we hope to see you soon.”