A spokesperson for the fast food chain confirmed the staff affected work at the Pollokshaws restaurant and are self-isolating at home, in line with government guidance.
The spokesperson said: "It goes without saying we’re wishing them a full and speedy recovery.
"We’ve been in close contact with the Public Health Protection Unit from NHS Greater Glasgow & Clyde and we’ve taken the decision to close the restaurant for two weeks as a precaution.
"We’re doing all we can to support our teams at this time and continue to work closely with local authorities to make sure we reopen our restaurant only when it’s safe for both guests and team members.”
The latest Scottish Government statistics, published this afternoon, show 68 further coronavirus cases have been confirmed in Glasgow in the last 24 hours.
Restrictions have been reimposed on people living in three council areas - City of Glasgow, East Renfrewshire and West Dunbartonshire - visiting other households due to a recent rise in cases in the area, home to about 800,000 people.
A total of 141 new positive cases have been confirmed across Scotland, representing 1.5 percent of all newly tested individuals.
No new deaths have been recorded in the past 24 hours, meaning the death toll remains at 2,496.
Weekly data from the National Records of Scotland says 4,228 people have died where the virus was mentioned on the death certificate.