As of Friday evening around 30 firefighters were still inside the building using thermal imaging equipment to assess the damage caused by what the fire service described as a "deep-seated fire within the structure".
Police are diverting traffic around the area and officials from the council's building control department are also at the scene.
A number of other commercial properties on Sauchiehall Street have also been closed as a precaution, and concerns have been raised that the Galleries will not re-open in time for Saturday shopping.
There were no reports of injuries.
The fire was identified as having broken out in a wall cavity on the ground floor of the mall.
Fire alarms sent an automated signal to the fire service around 10.40am, with workers and shoppers being evacuated soon after.
One Galleries worker said: “We had been standing outside for two hours when the centre management took all the store managers aside. They were all escorted inside by fire officers to allow them to collect any handbags and personal belongings and to put till money in the safe.
“We’ve been told we won’t get back in today and possibly not tomorrow either. Some workers are going to work at other shopping centres or stores but a lot are being told to go home.”
A spokesman from Strathclyde Fire and Rescue said: “The centre was safely evacuated and crews investigated the source of the smoke.
“They identified a deep seated fire within the structure and began work to access and extinguish it.
“Police Scotland are in attendance for traffic and crowd control and both the centre and several commercial properties on Sauchiehall Street have been closed as the emergency services operation continues.
“Glasgow City Council building control are at the scene and the incident is likely to be ongoing for some time.”
A spokeswoman from Buchanan Galleries said: “We can confirm a fire has broken out in a cavity wall on the ground floor of Buchanan Galleries.
"Fire service remain on site and have advised that Buchanan Galleries will not reopen Friday 23 August."