The 26-year-old victim encountered the suspect on a northbound No. 3 train just after 9:30 p.m. Sunday.
A dispute ensued, and the suspect pulled out a knife and slashed the man in the forehead and the right hand, according to police.
The victim got off at the 72nd Street station on the Upper West Side and was taken to St Luke's Hospital for treatment of the non life threatening wound.
The suspect remained on the train. No arrests were made.