Sebastian Zapeta, 33, who federal immigration officials said is a Guatemalan citizen who entered the US illegally, was not required to enter a plea and did not speak at the hearing in Brooklyn criminal court.
He will remain jailed at the city's Rikers Island complex and is due back in court on Friday. His lawyer did not ask for bail.
Zapeta is charged with two counts of murder, accusing him of intentionally killing the woman and killing her while committing arson. He is also charged with one count of arson. The top charge carries a maximum sentence of life in prison without parole.
Brooklyn District Attorney Eric Gonzalez called the attack a "gruesome and senseless act of violence" and said it would be "met with the most serious consequences."
The apparently random attack occurred Sunday morning on a train stopped at the Coney Island station. The victim's identification is still pending.
Authorities say Zapeta approached the woman, who may have been sleeping in the train, and set her clothing on fire with a lighter.
Zapeta then fanned the flames with a shirt, engulfing her in fire, Assistant District Attorney Ari Rottenberg said in court Tuesday.
Zapeta sat on a bench on the subway platform and watched, Rottenberg said.
According to Rottenberg, Zapeta told detectives that he didn't know what happened but identified himself in images of the attack.
Zapeta's lawyer, public defender Andrew Friedman, did not speak to reporters after the arraignment.
Video on social media appears to show some people looking on from the platform and at least one police officer walking by while the woman is on fire inside the train.
NYPD Transit Chief Joseph Gulotta said Sunday that several officers responded to the fire and one stayed to keep the crime scene "the way it's supposed to be" while the others went to get fire extinguishers and transit workers.
"Officers who were on patrol on an upper level of that station smelled and saw smoke and went to investigate. What they saw was a person standing inside the train car fully engulfed in flames," Police Commissioner Jessica Tisch said.
They eventually put the fire out, but "unfortunately, it was too late," Tisch said, and the woman was pronounced dead at the scene.
Zapeta was taken into custody Sunday afternoon while riding a train on the same subway line after teenagers recognised him from images circulated by the police.
A Brooklyn address for Zapeta released by police matches a shelter that provides housing and substance abuse support.
Federal immigration officials said Zapeta was deported in 2018 but later reentered the US illegally.
The crime deepened a growing sense of unease among some New Yorkers about the safety of the subway system, amplified by graphic video of the attack that ricocheted across social media.
Overall, crime is down in the transit system compared to last year.
But murders are up, with nine killings this year through to November compared to five during the same period last year.
There have also been several high-profile incidents, including one in September where police inadvertently shot two bystanders and a fellow officer when they opened fire on a man holding a knife in front of a train.
Earlier this month, a Manhattan jury acquitted former Marine Daniel Penny in the chokehold death last year of an agitated subway rider. The case became a flashpoint in debates over safety, homelessness and mental illness on the system.
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