56-year-old Rupert Smith was killed in the blaze that broke out just after 10 p.m. in a six-story apartment building on Kingston Avenue in Crown Heights.
Investigators say the fire broke out in Smith's second-floor apartment and spread.
When firefighters arrived, the fire was out the second-floor window.
Once inside, firefighters found Smith in an apartment. He was unconscious and had burns all over his body.
Smith has a history of setting fires and that is part of the investigation, the FDNY said.
Residents had to quickly rush out to escape.
"I told the kids to go out. By the time I went back in to grab my robe, the kids were coming back up because they were overtaken by the smoke," said tenant Shatoya Killings. "So we had to make our way through the fire escape. But we couldn't get down because the ladder wasn't down so we had to stay at the bottom of the fire escape."
Four residents in the building were treated for smoke inhalation.