The Bell, on Lower Road in Stoke Mandeville, made an announcement on its Facebook page on Sunday that staff had been close to someone who had tested positive for the virus.
In a second post on Tuesday, The Bell suggests the person who tested positive had been in the pub.
As a result all customers who visited the pub on the same day have been contacted.
The pub has now announced it will be closed until Saturday September 5th.
A statement on The Bell's Facebook page thanked customers for their understanding. And staff also moved to reassure people they would have been contacted if they had been in the pub on the same day as the individual who tested positive.
"Dear all, firstly we are very happy to say that all of our members of staff have tested negative for Covid-19," The Bell's statement reads.
"Unfortunately as one of our staff members was close to the person who has tested positive we have taken the necessary precautions and decided to close The Bell until Saturday 5th September.
"Our customers health and well being remain the most important thing we must concentrate on so we hope you all understand the decision we have decided to make.
"We would also like to make everyone aware we have contacted the people who were in The Bell on the same day as the person who has tested positive. If you have not received communication from us you do not have to self isolate or book yourself in for a test, however, of course if you would like peace of mind, please do so.
"We thank you for your continued support and we hope to see everyone again when we reopen our doors to you all. Stay safe, and thank you. The Bell team.