Kante started in midfield for Didier Deschamps against Bulgaria but lasted just 33 minutes when he was replaced by Adrien Rabiot.
The news will be a concern for Chelsea boss Antonio Conte, who is already having to deal without Alvaro Morata.
Summer signing Danny Drinkwater is also injured but is understood to be closing in on a return.
After the international break Chelsea face Crystal Palace, hoping to bounce back from a disappointing 1-0 defeat to Manchester City.
Former Chelsea left-back Wayne Bridge is a big fan of Kante and has compared him favourably to Claude Makelele.
“Kante is just like having another Makelele back,” Bridge told The Sun.
“He won player of the year and has made a massive difference in terms of a defensive midfielder, the way he gets around the pitch tackling.
“They had Matic who could sit a little bit for them but Kante is a totally different player.
“He reminds me of Makelele so much when we did so well with him at Chelsea.
“He’s great for the team and he’s one of my favourite Chelsea players at the moment.”