Hamilton, who flew back home to Britain to join the team's celebrations after they won their second successive constructors' championship in Russia, has got into trouble previously for his champagne-spraying antics on the podium.
He was criticised and accused of sexist bullying in April for aiming a spray of champagne directly in the face of a Chinese Grand Prix hostess in Shanghai.
That incident, highlighted in photographs that showed the woman flinching, triggered condemnation in Britain and Germany as well as on Chinese social media but the hostess herself played it down.
Putin presented Hamilton with the winner's trophy on Sunday, with the Briton starting the traditional champagne spraying ritual before the president had left the podium.
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Photographs appeared to show dark flecks of champagne foam on the back of Putin's jacket as he departed.
Some media reports subsequently suggested Hamilton, who is now on the brink of a third drivers' title, had 'soaked' the Russian leader, leading to jokes on social media about what punishment the driver might suffer.
(Reporting by Alan Baldwin in Sochi, editing by Ken Ferris)
