Two men were arguing on the mezzanine of the 14th Street and Sixth Avenue subway station, police said.
One man slashed the other in the arm, according to the New York City Police Department.
The victim was taken to Bellevue Hospital with a non-life threatening injury.
The 22-year-old suspect, who is homeless and lives at the Bellevue Men's Shelter, is in custody. Charges are pending.
NYPD Chief of Detectives Robert Boyce said they believe the suspect knows the victim.