Crews battled a two-alarm fire at Tracey Towers in Bedford Park Tuesday morning.
Officials say they believe the fire broke out in the compactor room on the 24 floor of Building 20 just before 3 a.m.
Crews say heavy smoke traveled to other floors of the apartment building.
Resident Philip Amoah says he and his family were trapped on their balcony for hours.
"I touched my main door and it was hot and the smoke was coming in and we couldn't bare it. We had to come to the balcony and close the door," says Amoah. "My sister was screaming and I had to calm her down. Trying to calm other people down from saying we are dead."
Officials say 16 people suffered minor injuries, including one firefighter.
An FDNY response vehicle were set up as a temporary shelter for those who were displaced.
Within three hours fire officials were able to clear the 41-story building.
The cause of the fire in under investigation.