The crash occurred at 2001 Ventura Blvd. shortly before noon.
Oxnard police said an 86-year-old Oxnard resident was in the process of parking his 1989 Buick Regal and put the car in reverse, backing into six pedestrians.
The injuries ranged from minor to moderate. Two of those pedestrians were transported to a nearby hospital to be treated for their injuries, police said.
According to investigators, the driver remained at the scene and told authorities that he inadvertently placed his car into reverse and accelerated while attempting to park his vehicle in the parking lot.
Authorities do not believe alcohol or drugs were involved. The driver was not injured.
The crash remains under investigation. If you have any relevant information about this incident, you're urged to contact Officer Michael Wood at (805) 385-7750.