The fire appears to have started inside a trash compactor on the 24th floor of the Tracey Towers on West Mosholu Parkway in Norwood around 3 a.m.
Video from the scene showed residents screaming for help from balconies on lower floors.
The fire sent smoke throughout the building.
Thirty-four people, including two firefighters, suffered minor injuries. Officials said 22 people were taken to the hospital, while 12 were treated at the scene.
The cause of the fire is under investigation.
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