SFPD investigators identified the driver as Christopher Kohrs, 38, of San Francisco.
It happened at Broadway and Montgomery street at 2:20 a.m.
Officers found two pedestrians who had been struck by an orange Dodge Charger that had been left at the scene. Police said Kohrs abandoned his car and took off.
Witnesses said one of the pedestrians flew into the air after being struck.
The pedestrians, both males in their 40's, were transported to a local hospital with serious, but non-life threatening injuries and are expected to survive.
Witnesses described a scary scenario as they saw two men lying on the ground. "Some guy moves, but the other guy does not move. Then they take the guys in emergency," witness Allan Tahamouni said.
"The car was right here when I looked out, but I didn't see anyone get out of it or anything. All the doors were shut, the lights were on. It just looked like somebody had pulled up, stopped, got out of the car and left," witness Trey Bellomy said
Police wouldn't comment whether Kohrs was under the influence at the time of the accident.
Kohrs became a local celebrity and social media sensation last year when residents began posting pictures of him because of his good looks.