Indio Downey, 20, was taken into custody in West Hollywood on June 29 after police pulled over his friend's car, in which he was a passenger, reported Digital Spy.
The officers searched the vehicle and allegedly found cocaine in Indio's possession, prompting them to arrest him.
Downey Jr, 49, who has struggled with drug addiction in the past, said in a statement, "Unfortunately there's a genetic component to addiction and Indio has likely inherited it. Also, there is a lot of family support and understanding, and we're all determined to rally behind him and help him become the man he's capable of being.
The 'Sherlock Holmes' actor was arrested multiple times on drug-related charges, including cocaine, heroin and marijuana, between 1996 and 2001.