The victim, also a woman, was pushed onto the tracks as a southbound No. 1 train pulled into the Times Square station around 1 p.m. EST (1800 GMT), and she was pronounced dead on the scene shortly afterward. Witnesses immediately alerted police officers, who apprehended the suspect in the station.
Neither the victim nor the suspect was immediately identified by authorities.
"What happened here today is tragic," Joseph Fox, chief of transit for the New York City Police Department, told reporters at the midtown Manhattan subway station, one of city's largest and busiest.
The victim was standing on the platform when the suspect, wearing a pink shirt and scarf, lunged at her, police said.
Two hours after the incident, emergency responders were working to remove the woman's body from the tracks and resume subway service at the station before peak evening commuting hours.
Investigators were reviewing surveillance video and interviewing witnesses to determine a motive, said William Aubry, the police department's chief of Manhattan detectives.
Many of those who saw the attack were visibly shaken. Some witnesses said the victim and the suspect were involved in a dispute before the fatal shove, Aubry said, but it was not immediately clear whether the women knew each other.
Dozens of people are hit by New York City subway trains each year, although most of the incidents are accidental, according to the Metropolitan Transportation Authority, which operates the system.
Last year, a woman was convicted and sentenced to 24 years in prison for fatally pushing a man into the path of an oncoming New York subway train in 2012.