Sources told the Sun that Rocco was seen tossing something away as police approached him. When officers noticed traces of cannabis on his clothes they searched him and found a small quantity of cannabis.
He was arrested on September 28 and taken to a north London police station.
A police spokesman said: "A 16-year-old youth has been arrested for possession of cannabis. The arrest follows a stop and search by officers from Camden borough at around 5.15pm on Wednesday, September 28 at Steeles Mews North.
"The youth was taken to a north London police station. He was subsequently bailed and dealt with by Camden borough's Youth Offending Team.
"He was dealt with by way of Triage, which uses multiple strands to engage and educate young people in order to prevent re-offending."
The teenager has been at the centre of a bitter custody dispute between his director father and pop icon mother. The custody disagreement began in December 2015 during a falling out between Rocco and his musician mother when he abandoned her Rebel Hearts tour.
He refused to travel with Madonna and she launched legal action in the US and UK demanding custody of her son.
Guy Ritchie's lawyers argued Rocco was settled in school in London and in September he won the bitter nine month battle over where their son should live.
The Sherlock Holmes director reached a settlement with the pop star hours before they were due in court in New York and it was agreed the teenager would continue to live in London.
Website TMZ claimed that Madonna thought Guy "had poisoned her son against her" and, "as the disciplinarian [parent], she felt guy was way too permissive".
The terms of the custody agreement remain confidential, but it is understood Rocco is schooled in London, with regular visits from his mother.