Police say something flew through a windshield, hitting the driver, an extra who was also the owner of the car.
Police say the car kept going for a mile before finally stopping.
The driver was airlifted to the hospital. There's no word on the extent of the victim's injuries.
The movie stars Shia LaBeouf, Patrick Dempsey, Frances McDormand, John Malkovich and model Rosie Huntington-Whitely.
The Associated Press contributed to this report.