The fire broke out Friday around 9 p.m. in the building on 351 East 84th Street near First Avenue.
Officials say two other people were injured in the fire - one serious and one minor injury.
Sources say the victim, a 77-year-old man, is a smoker, and believed to have started the fire. He was found with burns lying in his bed.
His adult daughter was reportedly in the apartment with him and noticed the fire too late to do anything.