"Following tests carried out today by Real Madrid's medical department on our player Kylian Mbappe, he has been diagnosed with a hyperextension of the posterior capsule of his left knee," the Spanish club said in a statement.
The forward left the pitch shortly after opening the scoring in a 1-0 French win against Turkey on Friday.
New France coach Zinedine Zidane said France were "not going to take any risks" and that he would not use Mbappe in the three Nations League matches scheduled over the next 10 days.
France travel to Belgium on Monday before hosting Italy and Belgium at the Stade de France on October 2nd and 5th.
Real Madrid's first game after the international break, with Villarreal on October 10th, might be too soon for an Mbappe return, but Spanish daily AS reported Saturday that he would certainly be ready for the Classico with Barcelona on October 25th.