It is believed a rear wheel of the First-operated bus fell into a hole in the road caused by subsidence from a burst water main.
The incident happened early this afternoon.
Glasgow City Council said George Square will be closed between North Hanover Street and North Frederick Street at 7pm to allow the bus to be removed.
All traffic will be diverted north on North Hanover Street.
Eyewitness Billy Murdoch, 60, from Glasgow, said: “They have had engineers out taking photos of this since it happened.
“It looks like subsidence and the bus was tilting at quite an angle.”
The bus was stopped in a bus lane outside George House when it began to sink. No passengers were on board at the time.
A cordon was set up around the bus and police attended the scene.