The incident happened around 10:45 a.m. Thursday on a northbound D train south of the Bryant Park station, around 42nd Street and Sixth Avenue.
Authorities say there was an argument between two men that escalated into a slashing.
"One male produced a box cutter after they got into words, and the victim received slash wounds to the face, hands and chest area," Assistant NYPD Chief James Coogan said.
The suspect fled at the Bryant Park station.
"We do have witnesses that were aboard the train who we have, but we don't have any reason for the dispute, why they were arguing," Coogan said.
The 38-year-old victim was taken to Bellevue Hospital with what police said were non life-threatening injuries.
Irene Malinowski saw the injured victim when he came out of the subway.
"We really didn't know if more people were involved," he said. "But he looked like he was OK, just dripping from a lot of blood."
Charges are pending.