The car jumped the curb in the 1600 block of North Fair Oaks Avenue in Pasadena.
Police said the driver lost control of the car after swerving to avoid someone who was backing out of a driveway.
The victim, a woman in her 50s from a nearby convalescent home, was pinned between the car and a wall and was pronounced dead at the scene.
The driver, who was not hurt, is under arrest for vehicular manslaughter.
Police also want to talk to the driver of the car that was backing up.