Godoy was among two groups of males involved in a shooting in the 800 block of O'Farrell Street at about 9:40 p.m., Sgt. Dennis Toomer said.
Godoy was pronounced dead at the scene, Toomer said. A second victim was transported to San Francisco General Hospital with life-threatening injuries.
During the incident, a responding officer fired at one of the armed suspects, but did not hit him, according to police.
The suspect fled on foot, and the officer pursued him and took him into custody, according to Toomer. His name has not been released.
Two guns were recovered from the scene, Toomer said.
It has not been determined if the shooting was gang related.