Crews were called to the blaze at a building in Stewartville Street, in Partick, at about 12:15.
The fire broke out in a communal area of the block. Four people were treated at the scene for the effects of smoke inhalation.
The blaze triggered a large response from the emergency services.
A spokesman for the Scottish Fire and Rescue Service said: "On arrival crews found a well-developed fire on the third floor of a six-storey residential block of flats with residents unable to leave the building.
"Firefighters quickly brought the fire under control, whilst at the same time rescuing 17 people from the property, some of whom were suffering from slight smoke inhalation and minor injuries."
Crews worked through the night to deal with any fire spread and make the scene safe.
A spokeswoman for Police Scotland said: "About 25 to 30 persons were evacuated."
The Scottish Ambulance Service sent four resources from their special operations response team, two A&E ambulances and an ambulance car.
A spokesman said: "We did not transport anyone to hospital. We dealt with smoke inhalation."
Firefighters have rescued 17 people from a six-storey block of flats in Glasgow's west end after a serious fire left them trapped in the building.