The woman, who has not been identified, sat motionlessly aboard a stationary F train at the Coney Island-Stillwell Avenue subway station in Brooklyn at about 7:30am on Sunday when an unknown man calmly approached her and used a lighter to set her clothes on fire.
The New York Police Department said there was no interaction before the attack and they did not believe the two people knew each other.
The man got off the car as police officers on patrol in the station rushed to the blaze.
"What they saw was a person standing inside the train car fully engulfed in flames," New York Police Commissioner Jessica Tisch said at a press conference.
Mobile phone video published on social media by a horrified onlooker showed a man sitting on a bench on the platform a few steps away from the burning woman, dressed in a grey hoodie that resembles that worn by the suspect arrested later on Sunday.
Asked whether the man watching from the bench was the attacker, police said that responding officers had no reason to think he was a suspect when they rushed to the woman's aid.
The officers used fire extinguishers to put out the fire and the woman was pronounced dead at the scene by emergency responders, police said.
Police arrested a suspect, who has not been publicly identified, as he rode the subway later on Sunday.
Police said they were still investigating the victim's identity and the reason for the attack.
with Reuters
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