One person was taken into custody at the scene, the NYPD tweeted.
During the dispute, the driver got out of a white Hyundai Sonata and stabbed two people in the torso, the New York Police Department said in a statement.
The other people hit and the two people stabbed were in stable condition.
Police were searching for the driver, The Associated Press reported.
The driver then got back in the vehicle and drove onto the sidewalk about half a block away, striking six victims.
Ozzie Rogers, who witnessed the incident, told the New York Daily News that he saw the vehicle go at least 50 miles per hour on the sidewalk. "The bodies went flying". Four others who were struck are in critical condition.
Six people were struck by the vehicle, including the person who was killed.
Police have not released any information about the victims, the driver or the vehicle.
One person is now "in custody for questioning", but police are still looking for the driver of a white Hyundai Sonata in connection with the hit-and-run incident, a police spokesman said.