The victims are in stable condition at a local hospital after the shooting, which was reported at about 7:10 p.m. near the intersection of Bell Street and University Avenue, police said.
The victims were stopped at the intersection when the suspect approached the vehicle and started shooting, according to police.
The woman sustained a gunshot wound to her lower back while the 6-year-old girl received a gunshot wound to her foot. Another small girl and 5-month-old boy were in the vehicle but were not injured in the shooting, police said.
No arrests have been made, and police are investigating a motive for the shooting.
Anyone who may have witnessed the shooting is encouraged to contact police Detective Angel Sanchez at (650) 853-3144 or the East Palo Alto Police Anonymous Tip Line at (650) 851-8477.