Police say they were called to Flower Street on the city's northeast side around 4:15 Tuesday afternoon.
The victim has been identified as Santiago Velazquez, 57, of Rochester. Police say they were called to the area for the report of a person shot.
Investigators say two suspects and Velazquez were involved in a fight on the front steps of a house.
Velazquez was shot in the lower body, and the suspects fled the scene before police arrived. Velazquez was taken to Strong Hospital with non-life threatening injuries.