Authorities said the incident happened around 6:30 p.m. on the roof of a parking structure in the 600 block of South Carondelet Street.
A man was suspected of carjacking the victim and then running over the person. The suspect then fled the scene in the victim's vehicle.
Los Angeles police said they're looking for a gray Nissan X-Terra. No description was available for the suspect.
The victim is believed to have been in his 60s.
Authorities hope the parking structure has surveillance video that can help them with the investigation.