The Paris Saint-Germain forward crumpled to the floor after the challenge from Rami and remained on the ground for several minutes as the medical staff assessed the injury.
Mbappe, 19, hurt his left ankle and went back to the dressing room rather than continuing the session, according to L'Equipe.
The incident involving Mbappe and Rami sent social media into overdrive.
While France's first 2018 World Cup match against Australia is set to kick off on Saturday, nothing has been announced yet regarding the severity of the injury.
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Griezmann said: "We know it will be hard, but we have the squad and the dressing room to achieve something big".
France forward Kylian Mbappe says he's "fine" after he was forced to leave training early on Tuesday following a tackle by teammate Adil Rami. "I want to give the best of myself in the field, that is the most important, no matter where I play, I am at the service of the team".
The 1998 winners also face South American side Peru and fellow Europeans Denmark in Group C and they are heavy favourites to progress to the knockout rounds as winners.