The 45-year-old man, whose name was not immediately released, was outside 1875 Third Ave., near East 97th Street, when he got into an argument with a 30-year-old male acquaintance, an NYPD spokesman said.
The victim said he had been holding onto the suspect's bag for safekeeping, police said.
But the suspect threatened the victim before taking out a yellow box cutter and slashing him across the left cheek, police said.
The victim was treated at Mount Sinai, where he's listed in stable condition, police said Friday morning.
The suspect fled the scene and wasn't immediately arrested, police said.