Hundreds of customers and staff had to leave the mall when firefighters were called at about 10.40am today when smoke started spreading through the building.
They established that the flames were coming from inside a cavity wall and officers told the centre's management that it could not reopen today.
The fire service said it is a "deep-seated" fire within the structure of the building and around 30 officers are continuing to work to access and extinguish it.
There are no reports of any injuries.
Other nearby shops on Sauchiehall Street have also been closed and police are diverting traffic around the area.
Glasgow City Council building control officers are at the scene and it is likely to be on-going for some time, the service said.
It is understood a decision on re-opening will not be taken until Saturday morning at least.