The 20-year-old was pulled over by the Los Angeles Police Department on Sunday afternoon in what officers described as a suspicious vehicle. He was the only one in the car and was allegedly under the influence of drugs when he was stopped.
He was allegedly found with cocaine and drug paraphernalia in his possession.
Robert Downey Jr. and his son Indio in 2008
Indio was arrested immediately and bail was set at $10,250 in the early hours of Monday morning, E! News confirmed.
He is Robert's eldest child, and has a young step-brother who was born in 2012.
Robert, 49, struggled for work after his Oscar-nominated portrayal of Charlie Chaplin in the 1992 film Chaplin due to his battles with addiction, but has since overcome his dependency on drugs and alcohol to rise to the top of the A-list and the rich list in Hollywood.
He earned an estimated $75million (nearly £50million) in 2012, making him 2013's highest paid actor in Hollywood.
Indio Falconer Downey in 2011
In 2012, he did not even feature in the top 10 list but ended up overtaking the likes of Tom Cruise and Leonardo DiCaprio to the number one spot.
Speaking to E! News, the Iron Man actor said: "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."
Robert added: "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."