About 20 people were evacuated from their homes as the fire took hold of the four-storey building in Crow Road, Partick.
The alarm was raised at about 2.20am yesterday by a trapped resident. Thick smoke swirled throughout the block as firefighters used ladders to rescue four people. Five others were led to safety.
Paramedics treated some of the rescued for smoke inhalation.
Two children were taken to the city's Yorkhill Children's Hospital as a precaution. One woman, believed to be in her 40s, was taken to the Southern General Hospital, where she was described as "serious" with severe smoke inhalation and "significant" burns.