Authorities say 140 firefighters responded to the blaze at the six-story building on West 39th Street just after 4:30 p.m.
The four-alarm fire took several hours to extinguish.
Officials say 14 firefighters and one civilian suffered non-life-threatening injuries.
"The injuries were due to fallen debris and heat exhaustion, on a day like today these conditions are very difficult for the firefighters," FDNY Chief James Booth said. "Everyone who is injured is stable at this time."
The cause of the fire was not yet known.
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