Police said the unnamed woman was riding the subway at the Coney Island-Stilwell Avenue station in Brooklyn around 7:30 local time when a man approached her.
Police said there was no interaction prior to the attack and added that they did not believe the two men knew each other.
The man got off the train as police officers on patrol at the station rushed to the scene of the fire.
“Officers were patrolling the upper part of the station when they noticed the smell and smoke and went to investigate,” Mr Tisch said.
“What they saw was a person standing inside the train completely engulfed in flames.”
Police are investigating the victim’s identity and motive for the attack.
