Three families are reported to have been living in the house in the Bromma suburb in western Stockholm.
"It seems that several of them are seriously injured," chief fire officer Tony Frank told Swedish Radio.
Emergency services confirmed that 12 children and adults have been taken to hospital for treatment for broken bones and smoke inhalation.
The alarm was raised shortly before 11pm and the fire, which is believed to have started on the top floor, was under control on Friday morning.
Police are investigating the cause of the blaze and have not ruled out arson.