The blaze broke out in a ground-floor flat of a four-storey tenement in Tollcross at about 22:50 on Monday.
One woman was rescued from the top-floor flat in Fairburn Street and eight people were injured in total.
The other five people were treated in hospital for minor injuries before being released. Police said there were also reports of an explosion.
Dozens of people were evacuated from their homes and about 50 firefighters were involved in tackling the blaze.
The cause of the fire is being investigated.
The Red Cross helped at the scene to look after residents who had been evacuated.
A Scottish Fire and Rescue Service spokesman said: "The service received a 999 call from a member of the public shortly before 11pm alerting them to a fire within the ground floor of the four-storey tenement building.
"Local fire crews from Clydesmill, Calton and Polmadie where immediately dispatched and on their arrival were met with a well-developed fire.
"The incident commander immediately requested further resources to deal with the fire and attend to casualties at the scene."
Two men and a woman are seriously ill in hospital after a fire in the east end of Glasgow.