It happened on Beach 129th Street in Rockaway Saturday morning.
It took nearly two hours for firefighters to get the blaze under control.
Of those 13 firefighters suffering minor injuries; one fell through a floor and another was forced to climb out a window on a rope because of the intensity of the blaze.
"He had already deployed his personal safety system, which is a rope that can attach to a substantial object to get out the window. You could tell he was a very well-trained firefighter. He got out of the window in like 30 seconds and that saved him from serious injury," FDNY Deputy Chief Jim Didomenico said.