Fire crews from the south side and east end of the city were called to the three-storey tenement in Maxwell Road, in the Pollokshields area, shortly before 10pm after receiving 15 repeat calls from members of the public.
A spokesman for Fire and Rescue Scotland said crews arrived to find a "well-developed blaze".
Witnesses reported seeing at least four fire appliances, three ambulances and police vehicles.
Firefighters used aerial apparatus and rescue platforms to pluck people from the tenement.
The spokesman said: "Because of the extensive damage in the roof space 12 families have been evacuated at this point.
"There are no injuries or casualties except for one female who was treated for smoke inhalation as a precautionary measure."
The cause of the fire was unknown but the spokesman said a full probe was due to be carried out by fire investigation teams once the blaze was under control.