Around 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 around 2.20am today by a resident trapped by the smoke.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.
Another woman and two men were taken to the city's Western Infirmary where they were also treated for smoke inhalation.
At the height of the blaze, around 35 firefighters were at the scene.
The affected residents were this morning prevented from returning home, many having spent the night in Patrick Burgh Halls or with family.
This morning, firefighters were still at the scene with smoke still evident in the building.
Part of Crow Road, near Dumbarton Road, remained sealed off as fire investigators examined the property. The cause of the blaze is not yet known.