It meant Tottenham's Moussa Sissoko came into Didier Deschamps' line-up for the Group H fixture, which France won 1-0.
"He felt a pain in his adductor muscle," Deschamps said after the game.
"He had a feeling where he didn't feel comfortable to play. I made the decision [to remove him from the team], because maybe it could get worse.
"I knew Moussa would be ready.
"I do not think it's too serious for [Kante], but I do not have an answer [to whether he'll play against Turkey on Tuesday] tonight."
Kante's absence would be a concern for Deschamps as he's already missing Kylian Mbappe, Hugo Lloris and Ousmane Dembele.
The midfielder's club side will also be sweating over his fitness.
Chelsea boss Frank Lampard will hope the former Leicester man is fit for the Blues' next Premier League clash, their home game against Newcastle on October 19.
The 28-year-old has started just three of Chelsea's opening eight league games after being troubled by an ankle injury in the early weeks of the season.
Kante missed three weeks of Premier League action as well as his side's Champions League opener against Valencia, while he was also kept out of the France squad for the previous qualifiers in September at Lampard's request.
The Blues have won their last four matches in all competitions heading into next week’s game at Stamford Bridge, which is followed by a trip to Amsterdam, where they face Ajax in the Champions League on October 23.