Officers found the victim around 4:30 am on Saturday near Mooney Boulevard and Noble Avenue.
Police said the person had been sleeping in a parking area near a business.
Investigators believe a driver pulled into the lot and stopped for a moment with their headlights shining on the victim. That's when the driver then sped up and ran over them.
The driver then drove away from the parking lot.
Police say the victim was taken to the hospital with several injuries. Their condition has not been released.
Police have not yet provided a possible suspect description.
Anyone with information is asked to call the Visalia Police Department.