Al Gore III, 24, was driving a blue Toyota Prius about 100 mph south on the San Diego Freeway when he was pulled over by sheriff's deputies who said they smelled marijuana, said Sheriff's Department spokesman Jim Amormino.
The deputies searched the car and found less than an ounce of marijuana along with Xanax, Valium, Vicodin and Adderall, which is used for attention deficit disorder, Amormino said.
"He does not have a prescription for any of those drugs," Amormino said.
Gore was being held in the men's central jail in Santa Ana on $20,000 bail.
Kalee Kreider, a spokeswoman for his parents, did not immediately return phone messages to The Associated Press on Wednesday.