It said the platforms showed a senior government official sailing on a yacht with a billionaire oligarch, who has links with the former Trump campaign manager Paul Manafort.
Russia’s state-controlled media watchdog, Roskomnadzor, on Saturday ordered that 14 Instagram posts and seven YouTube videos be deleted.
He said the posts showed metals magnate Oleg Deripaska on a yacht with a Russian deputy prime minister, Sergey Prikhodko, and a woman who has described herself as an escort.
The watchdog listed the posts on its register of banned sites after Deripaska won an injunction from a court in his hometown Ust-Labinsk, which ruled they violated his privacy.
Roskomnadzor said it had informed the sites that they must delete the images within three days.
The images are at the heart of the public battle between Deripaska and the anti-corruption activist Alexey Navalny, who first drew attention to the posts in an investigative video piece he released last week.
In the report, he accused the oligarch of bribing Prikhodko by hosting him on the yacht in August 2016.