Crews rushed to the scene in Ardencraig Drive, Castlemilk, at around 10.20pm on Thursday.
Three children were among those rescued from the three-storey building.
Paramedics treated all seven people for smoke inhilation at the scene. They were then taken to the Victoria Infirmary.
Fire chiefs said the fire started in the close of the building.
Group manager Brian Winter said: "Firefighters led six people - three children, a woman and two men - to safety after quickly extinguishing the flames.
"All seven casualties were cared for by firefighters and paramedics at the scene before being taken by ambulance to the Victoria Infirmary.
"Specialist fire investigation officers attended and are liaising with police."