Police said the woman, whose name has not been released, was in a subway car at the Coney Island Stilwell Avenue station in Brooklyn around 07:30 local time (12:30 GMT) when a man approached her.
There was no interaction before the attack, police said, adding that they do not believe the two men knew each other.
The man got off the train when police officers patrolling the station rushed to the fire.
“Officers were patrolling the upper level of this station and smelled and saw smoke and went to investigate,” Ms Tisch said.
“They saw a man standing in a train car completely engulfed in flames.”
Police are still investigating the identity of the victim and the motive for the attack.
