Aldershot Garrison Sports Centre has closed until further notice after a visitor tested positive for coronavirus.
The person visited the Hampshire complex last Tuesday.
It is believed to be the first reported case of coronavirus involving the UK Armed Forces.
An Aspire Defence Services Limited spokesperson told Forces News: "Aldershot Garrison Sports Centre has been closed today after a recent visitor to the Centre tested positive for Coronavirus.
"This closure is at the instruction of Garrison Command."
The centre will remain closed on Tuesday and the garrison management team are continuing to seek advice from Public Health England, a further statement read.
External facilities are said to be unaffected.
Military sports events due to take place at the centre in the coming days have been cancelled, including basketball and martial arts.
The centre is open to both civilians and military personnel.
A Number 10 spokesperson said: "The Chief Medical Officer and the Public Health England team will be providing up-to-date advice for the Armed Forces and I would expect them to take decisions based upon that."
As of 9am on Monday, 319 people have tested positive for COVID-19 - up from 273 at the same point on Sunday, the Department of Health said.
On Sunday, Public Health England confirmed there had been eight confirmed cases of coronavirus in Hampshire.
Four people in the UK have died so far.
Cover image: Aldershot Garrison Sports Centre.