Sheriff's Sgt. Dave Valentine says Indio Falconer Downey was taken into custody Sunday afternoon after a car he was in was pulled over in West Hollywood.
Valentine says Downey was booked on suspicion of possession of a controlled substance, believed to be cocaine, and possession of drug paraphernalia.
Two other people were in the car, but only Downey was arrested.
Downey was released shortly after 9 p.m. on $10,250 bail. A court date is set for Aug. 29.
Downey appeared in the 2005 movie "Kiss Kiss Bang Bang," which starred his father. An email sent to Robert Downey Jr.'s publicist was not immediately returned.