Emergency services rushed to the scene in Paisley Road West, Cessnock, after receiving several calls.
Firefighters received reports about the blaze around at 9.15am. Several calls were made and it was believed people were still in the building.
One adult male was rescued from the top floor flat. He suffered burns to his hands.
Two women and one man were also rescued and were suffering from mild smoke inhalation.
The ambulance service were on the scene. One patient was taken to the Southern General Hospital.
Fire and ambulance services were still on the scene mid morning.
Eight firefighters entered the building with breathing apparatus and two high pressure jets.
Fire engines from Maryhill, Knightswood, Polmadie and Govan fire stations all attended the incident.
It is believed a member of the public was the first to ring the emergency services.
It is still unknown which flat in the block the fire had started in.
A spokesman from Strathclyde Fire and Rescue said: "Firefighters were called to a house fire at a tenement flat on Paisley Road West.
"The call came in at 9.15am.
"People were believed to be in another flat in the building, on the top floor.
"An adult male with burns was rescued from the top floor flat and given first aid by firefighters."
A spokeswoman from the Ambulance service said they were still at the scene and one patient had been taken to the Southern General.