The fire was reported at a home on 56th Street just after 3 p.m. and spread to another home.
More than 100 firefighters responded to the scene to try to contain the blaze from spreading down the block.
At least 10 firefighters suffered minor injuries, officials said, but they believed all of the residents made it out OK.
"By the time we discovered a victim on the second floor, in the bathtub, we were able to get him down, we transported him immediately to the hospital and he was alive, but then at the hospital he succumbed to his injuries," an FDNY official said.
Neighbors said the victim was friendly and had lived in the apartment for decades.
"This guy was a sweetheart, he was a really nice guy, I feel really bad, I feel terrible," one neighbor said.
The cause of the fire is under investigation.