More than 100 firefighters battled flames early into the morning at 952 Rodgers Place in Longwood.
The FDNY says crews responded within three minutes, but by then the building was already engulfed in smoke.
Some residents say they have nothing left.
"My roommate came and knocked on the door saying there's a fire. When I opened the door, all I saw was a lot of smoke. So right away I panicked, all I was able to do was throw on slippers," said one resident. "We lost everything right now, so we don't know what to do right now."
At least one of the injuries was to a firefighter.
Neither are said to be life threatening.
The cause of the fire remains under investigation.