A woman has died after being set on fire in New York City's subway, police say, and a person of interest is in custody.

New York City police announced on Sunday, local time, that they have detained a man who is believed to have intentionally set the woman on fire while she was possibly asleep on a stationary train.

New York City Police Commissioner Jessica Tisch described the case as "one of the most depraved crimes one person could possibly commit against another human being".

Commissioner Tisch said the suspect and the woman, both of whom have not been identified, were riding a subway train without any interaction between them to the end of the line in Brooklyn at about 7:30am.

After the train came to a stop, surveillance video from the subway car showed the man "calmly" walk up to the victim, who was seated motionless and possibly asleep, and set her clothing on fire with what appeared to be a lighter.

The woman's clothing then "became fully engulfed in a matter of seconds," Commissioner Tisch said.

Police do not believe the two knew one another.

Officers on a routine patrol at the Coney Island-Stillwell Avenue subway station smelled and saw smoke and discovered the woman on fire, standing in the middle of the subway car.

Emergency medical personnel declared the woman dead after the fire had been extinguished.

The suspect had remained at the scene and was seated on a bench on the subway platform, just outside the train car, Commissioner Tisch said, while police rushed to the subway car.

Body cameras worn by the officers caught a "very clear, detailed look" at the suspect and those images were published in the hope of finding him.

Transit police arrested the man after receiving a report from three high school students who had recognised the suspect from police images.

The man had a lighter in his pocket when he was taken into custody, Commissioner Tisch said.

NYC police said the investigation was continuing, including whether the woman was homeless and the background of the suspect.

AP