A Daly City police officer working an off-duty assignment at Century Theatres on Junipero Serra Boulevard first reported the shooting at 10:43 p.m., police Sgt. David Mackriss said.
The shooting occurred in the area of Pacific Plaza, which is located at 2001 Junipero Serra Blvd., after an altercation between the suspect and the victim.
Police said none of the injuries were reported to be life threatening.
The suspect fled through a pedestrian tunnel leading to the Daly City BART station, Mackriss said.
No arrests have yet been made, and police are looking for the man, who is of unknown race and is approximately 20 years old.
Anyone with information is asked to call investigators Detective Frank Mangan or Detective Ron Harrison at (650) 991-8098.