Los Angeles police said the husband was driving the black Lexus sedan in the 8300 block of S. Central Avenue shortly before midnight when a person in another vehicle started shooting at the victims.
The driver of the family's vehicle drove two blocks to the parking lot of a shopping center and stopped.
The woman, who was struck multiple times, died at the scene, police said. The man was sent to a nearby hospital in stable condition with unknown injuries.
Police said the man's two children, ages 3 and 5 years old, were inside the car but were not hit by gunfire. The 5-year-old was treated for minor cuts.
The suspect fled the scene and remained at large Monday evening. Descriptions of the gunman and the gunman's vehicle were not immediately available.
Police said the shooting was gang-related, but it was unclear who had been the intended target.