The incident happened at the Food Maxx store on Ben Maddox in Visalia early Saturday morning.
Police say eight people got into a fight in the store's parking lot.
Investigators say during the incident 22-year-old Ai Bou Seechan tried to drive away but hit a Honda and two people.
Both victims were taken to the hospital with minor injuries.
Seechan was arrested for drunk driving and assault with a deadly weapon.
