Police said the woman, who has not been named, was in a subway carriage at the Coney Island-Stillwell Avenue station in Brooklyn at about 07:30 local time (12:30 GMT) when a man approached her.
There was no interaction before the attack, police said, adding that they did not believe the two people knew each other.
The man got off the train as police officers on patrol in the station rushed to the fire.
“Officers were on patrol on an upper level of that station, smelled and saw smoke and went to investigate,” Ms Tisch said.
“What they saw was a person standing inside the train car fully engulfed in flames.”
Police are still working to identify the victim and the motive for the attack.
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