The FDNY responded to the call at about 8:30 a.m. at 781 Washington Avenue, a 7-story residential building in Prospect Heights.
The fire was placed under control about 90 minutes later, with about 100 firefighters responding.
The blaze broke out on the fourth floor of the building.
One civilian was taken to Cornell Hospital for a minor injury.
Residents, many of them elderly, said that because there is no central fire alarm in the building, it was a miracle that they got out.
Conditions in a third floor hallway became unbearable in a matter of minutes.
"No alarm, the alarm don't ring, the alarm started ringing when everybody was out already," said resident Angelita Rivera.
"The hallway was literally, you could not see your hand in front of your face. Also very heavy heat conditions, they were faced with adverse conditions and they got separated in that confusion up in the hallway," said Assistant FDNY Chief James Leonard.
Adding to the confusion, firefighters say, was that there is some renovation going on in the building and they weren't that familiar with the situation in the hallway.