Hamilton, who has more than four million followers on the social network - comfortably more than any driver in the sport - uploaded on-board footage of his pole position lap at the Chinese Grand Prix earlier this month.
American company Liberty Media have made the expansion of F1 on social media one of their main priorities since their £6.4billion purchase from private equity firm CVC Capital Partners in January.
But Hamilton, second behind Sebastian Vettel in the championship after he trailed the Ferrari driver in Bahrain on Sunday, was told to take down the video after breaching the sport's strict guidelines.
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Hamilton did not realise he was in infringement of the rules and removed the post as soon as he was asked.
"This season, Formula One has issued a new set of social media guidelines allowing teams and drivers to film and record their activities so as to bring the sport closer to the fans," a spokesperson for Liberty Media said.
"All teams and drivers have embraced this approach with enthusiasm, resulting in a surge of interest in F1 across social media.
"However, F1 does not want drivers posting international feed footage as this has been licensed to broadcasters' partners, in many cases exclusively.
"All teams and drivers have a clear understating of this and whenever a mistake is made, teams and drivers are asked to take down any relevant footage."
It is not the first time Hamilton, 32, has been in hot water for footage posted to social media. In the summer of 2015 he faced criticism for uploading a video at a Colorado shooting range on the same day a gunman attacked a train in France.
And on the eve of last season he was investigated by New Zealand police for posting a video while he was riding a motor bike. Both were taken down.
Hamilton is seven points behind Vettel after the opening three rounds of the new season. The next race takes place in Russia a week on Sunday.
