Another person was taken to the hospital for injuries from smoke inhalation and five others were treated by emergency personnel on the scene, reports news agency TT.
The apartment that burnt was on the eleventh floor and spread to the floors above and below. All three floors were smoke-filled.
A fireman was injured in the hand during the rescue operation and was taken to the hospital, reports Newspaper Aftonbladet.
It is unclear what caused the fire that started just before 11.00pm Friday night. It took firemen an hour to put out the fire.
“Police investigators will start their work when they can enter the apartments,” Mats Kömer, rescue leader with the Stockholm Fire Department, told Aftonbladet.
Residents living on the tenth, eleventh, and twelfth floors were evacuated.
Police and firemen from two departments responded to the emergency and an ambulance helicopter was on the scene as well.