Fire crews were called to the four-storey tenement block in Dowanhill Street, at around 4.30am this morning.
Residents from seven flats in the block were led to safety by firefighters wearing breathing apparatus.
The fire is thought to have started in a launderette in the basement of the building.
Crews from Cowcaddens, Maryhill, Yorkhill and Polmadie tackled the blaze.
No one was injured during the blaze. Strathclyde Fire and Rescue said a full investigation was under way to establish what caused the fire.
However police said it is not thought to be suspicious.
Fire crews were still at the scene at 10am, checking for any signs of fire and ensuring all pockets had been extinguished.
All windows in the tenement block had been left open and signs of smoke damage were still visible.
Residents were evacuated from three flats on the first floor, two on the second floor and two on the third. It is not known when they will be allowed to return to their homes.
A spokesman for Strathclyde Fire and Rescue said: "At present the firefighting operations now mainly consist of stripping down damaged material to check for any signs of fire spread and ensure all pockets of fire are extinguished.
"The cause of the fire is unknown and a full investigation is under way."
On Sunday, three people including a child were taken to hospital after a blaze broke out at a Paisley flat.
Firefighters were called to the property in Schaw Road in the Gallowhill area at around 12.15pm on Sunday.
Crews used a high pressure hosereel jet to douse the flames, which had taken hold in the kitchen of the property.
One man was taken to the Royal Alexandra Hospital suffering from smoke inhalation.
A woman and small child were also taken to the hospital for precautionary check-ups.