British Transport Police (BTP) were called to the scene just after 1am on Tuesday.
The station remains closed while police investigate but the inner and outer circles of the Subway are running and all other stations are open.
A BTP spokesman said: “British Transport Police were called to Bridge Street Subway station, Glasgow, at 1.12am this morning following reports of a burglary at the ticket office.
“Officers attended and three young men were arrested in connection at 1.51am.
“They have been taken to custody for questioning, where they remain.”
Glasgow Subway Travel tweeted: “Bridge Street Stn will not open this morning due to a police incident overnight.
“Both inner and outer circles are running and all other stations are open. Services will not stop at Bridge Street and the public will not be able to access.
“Nearest station is St Enoch.”