The blaze at the former Herald building in Albion Street began on the sixth floor, causing smoke to spread to other areas of the building.
Police Scotland said the road was closed at the Ingram Street/Albion Street junction and residents were evacuated while firefighters tackled the blaze.
A spokesman said: “Police Scotland officers are assisting with the evacuation of the building. The residents of the flats are being accommodated at the City Halls.”
A spokesman for the Scottish Fire and Rescue Service said: “At 9.04am on November 25, the service was alerted to a fire alarm activating at a block of residential flats on Albion Street in Glasgow.
“This was a fire on the sixth floor which had spread smoke to other areas of the building.
“Firefighters in breathing apparatus were able to extinguish the fire and conduct a thorough search of affected properties.”
Crews remain at the incident and are working to make the scene safe.
No injuries have been reported.