Police say Berta Booker, 49, died Sunday after being severely burned.
FDNY Marshals said their investigation indicates the fire in the Belmont section was intentionally set.
The FDNY is calling the fire "incendiary".
One other person was injured in the fire, officials say.
The fire broke out inside a unit in a five-story apartment building on the 2200 block of Adams Place in the Belmont section around 1:30 p.m. The fire was under control shortly before 3 p.m.
Neighbors living in the building say they heard a loud fight in the apartment where the fire started, and then the smoke detectors went off.
"The fire alarms were going off, there was smoke coming out of the window, and there was people on top of the roof," said Donzellastine Brown.
Emergency responders found a 44-year-old man with severe burns. He was transported to St. Barnabas Hospital and pronounced dead. His identity has not yet been released.
A 50-year-old man who suffered a foot injury is in stable condition.
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