The alarm was raised at 04:30 on Saturday after the property in a tenement block in the Cathcart area caught fire.
Firefighters wearing breathing apparatus entered the building in Holmlea Road to rescue the group.
The Scottish Fire and Rescue Service said six people were taken to hospital suffering from smoke inhalation.
A spokeswoman for the fire service said: "Both children went to the Royal Hospital for Children, two adults were taken to the Queen Elizabeth University Hospital and two went to Glasgow Royal Infirmary.
"They were treated for slight smoke inhalation. The seventh person did not require hospital treatment."
A total of four fire engines and one high-reach appliance were used to fight the blaze in the four-storey block of flats. The fire was extinguished shortly after 05:00.
The surrounding properties were evacuated and the road was closed during the incident.
Firefighters have rescued five adults and two children from a fire at a flat in Glasgow.