Anyone who was working or drinking at the Crown & Anchor in Stone on 16, 17 and 18 July is being told to get tested for COVID-19 following the confirmation of 10 positive cases.
Hundreds of people are reported to have turned up to a coronavirus walk-in centre in the town on Wednesday in the wake of the outbreak.
Staffordshire County Council said an individual who tested positive from the pub then went to a private social gathering, further spreading the virus.
In a post on Facebook, the pub said it had decided to temporarily close "due to the overwhelming amount of people visiting".
It is reviewing its risk assessment "to deal with the difficulty that we faced with social distancing" - but plans to reopen this weekend.
A walk-in centre for those without coronavirus symptoms opened in the Crown Street car park on Wednesday.
It is due to open again on Friday, from 10am until 5pm.
No appointment is required and the tests are free - but people are being asked to try and space out their visits.
A resident who did not want to give their name described queues of people for tests, adding: "Hundreds of people have already been down there, and it only opened this morning."
Anyone who does have symptoms is being urged to get tested also, by visiting the gov.uk website or calling 119 to make arrangements.
Dr Richard Harling, director for public health at the county council, said: "As part of our outbreak-control duties, we are dealing with an outbreak at the Crown & Anchor pub in Stone.
"It is important that anyone drinking or working in the pub on that weekend gets tested as soon as possible, which is why we've organised for a mobile testing unit to be in the town all day Wednesday and Friday."
He added: "We also want people who have been in close contact with anyone drinking in the pub on that weekend to get themselves tested, as well as people who were out and about in the town and are experiencing COVID-19 symptoms - namely a high temperature, new persistent cough or loss of taste and smell.
"It is also crucial that people self-isolate if they are told to do so.
"By getting tested, this gives us important information on the full extent of any outbreak, and allows us to put measures in place if needed to help prevent the spread of infection.
"We're doing everything we can to prevent outbreaks and stop the virus from spreading.
"Residents can help by continuing to follow the rules to stop the spread of COVID-19 - washing hands regularly, keeping your distance and wearing face coverings in shops and on public transport."
Speaking to the BBC, Dr Harling said "not very much was known" about the private social gathering that spread the virus further.
He said: "It does appear that one of the people who caught the infection at the Crown & Anchor was then at a private event where there was further transmission of the infection.
"This appears to largely be a young adult demographic, young adults in the 18-21 age bracket."
Stafford Borough Council, which administers the pub's licence, said there is a "possibility" that it could be reviewed "in due course".