It is believed the Paris Saint-Germain forward was caught by Marseille defender Adil Rami in a heavy challenge.
The session was broadcast live on YouTube by the French Football Federation but although Mbappe required several minutes of attention before returning to his feet, no update was released in the following hours until the 19-year-old posted on social media last night.
But Mbappe took to Twitter after the incident, saying: "I'm fine, it's just a knock so it doesn't matter but thank you for your messages. And let my friend Rami [know] it was not nasty".
France open their World Cup campaign on Saturday, and it appears Mbappe is now a doubt following an injury sustained in training.
Earlier this week, Mbappe played down another "knock" he received in Les Bleus' 1-1 draw with the United States in their final World Cup warm-up on Saturday, while coach Didier Deschamps spoke out in defence of goalkeeper and captain Hugo Lloris following his error in Lyon.
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.
The 19-year-old star enjoyed an excellent debut season at PSG, scoring 21 times and setting up 16 in 46 games in all competitions.