The Scottish Fire and Rescue Service (SFRS) was called to the scene on Skirving Street in Shawlands shortly after 8:30am today.
Four fire engines and an aerial appliance were sent to tackle the blaze, which was extinguished around an hour later.
Crews helped two people from the building and passed them on to the Scottish Ambulance Service.
It is understood one person has been taken to hospital.
A SFRS spokesman said: “The Scottish Fire and Rescue Service was alerted at 8:33am on Wednesday 3 April to reports of a fire within a first floor flat in a four-storey block on Skirving Street, Glasgow.
“Operations control mobilised four fire engines and an aerial appliance to the scene, where firefighters assisted two people from the building before handing them into the care of the Scottish Ambulance Service.
“The fire is now extinguished and crews remain in attendance as they work to make the area safe.”