Les Bleus take on Roberto Mancini's Italy in Milan on Thursday as they bid to strengthen their grip on top spot in Group A1, before facing Turkey in Bordeaux on Sunday.
"He will miss tomorrow, he felt a little pain and we won't take any risk," said Zidane.
"It's a shame to lose players but it's part of the game. I hope that it's nothing too serious and that he'll be available for Sunday... It's just a minor issue."
The Real Madrid forward is back in the France squad for this camp after missing their last three matches through injury.
He has already netted 17 goals in all competitions for his club this season.
France boss Zidane generates 'electric atmosphere' with Nations League wins
Mbappe scored the winning goal in Zidane's first match as coach, against Turkey in September in the Nations League, but had to leave the pitch shortly afterwards due to pain in his left knee.
After three wins and a draw in four group games, victory over Italy would see France qualify for the quarter-finals.
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