The accident happened around 7:10 p.m. at the intersection of Grand and Walnut avenues.
The 40-year-old woman and the girl were walking south across Grand Avenue in a crosswalk when they were hit by a westbound 1997 Audi sedan driven by a 26-year-old San Bruno woman, according to police.
Emergency responders found both pedestrians down in the roadway, and transported them to San Francisco General Hospital.
The girl's right arm was broken, but her mother suffered only minor injuries, police said.
Police said it appears the glare from the setting sun had prevented the driver from seeing the pedestrians. The driver will not be charged with a crime, police said.
The incident occurred during the tail end of Sunday's partial solar eclipse.