The Mercedes driver uploaded footage of his pole lap in China to Instagram before Liberty Media representatives ordered that it be taken down because it violated guidelines intended to protect its broadcast partners.
In a statement the company said: “Formula One has issued a new set of social media guidelines allowing teams and drivers to film and record their activities to bring the sport closer to the fans.
“However, F1 does not want drivers posting 'international feed footage' as this has been licensed to broadcaster partners, in many cases exclusively.
“Whenever a mistake is made, teams and drivers are asked to take down any relevant footage.”
Following its £6.4bn takeover of Formula One, Liberty Media introduced more relaxed social media regulations for teams and drivers in a bid to strengthen the entertainment and commercial value of the sport and stimulate more engagement among fans.
The guidelines do not however allow for any on-track footage or images to be posted as it belongs to broadcasters and Liberty Media is keen to protect and strengthen the value of future broadcast deals.
The new rules follow on from comments made by F1 chief executive, Chase Carey, who said the outdated social media regulations curbed Formula One’s ability to market itself and connect with fans on key platforms.
Hamilton, who has 3.8 million followers on Instagram and 4.16 million on Twitter, has been one of the most active drivers in taking advantage of the new guidelines. During pre-season testing Hamilton and other drivers began posting footage from inside and around the pit-lane for the first time.