Downey Jnr - who also battled addiction but managed to revive his Hollywood career and go on to star in Iron Man and the Avengers franchise - spoke out in defence of his son.
"Unfortunately, there's a genetic component to addiction and Indio has likely inherited it," he said in a statement to The News.
"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," he added.
"We're grateful to the Sheriff's department for their intervention, and believe Indio can be another recovery success story instead of a cautionary tale."
Downey, a first-time offender, was booked for cocaine possession and released hours later on $10,000 bail, but is due to appear before court on 29 August, prosecutors said.