France travel to Milan looking to strengthen their position at the top of Group A1, but will have to do so without their influential forward.
Mbappe reported discomfort during training, prompting Zidane to rule him out rather than risk aggravating the injury.
"He will miss tomorrow, he felt a little pain and we won't take any risk," Zidane said.
"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."
France face Turkey in Bordeaux on Sunday, with Zidane hopeful that Mbappe will recover in time to feature.
The forward has returned to the national squad for this international break after missing France's previous three matches through injury.
He has enjoyed an impressive season at Real Madrid, scoring 17 goals in all competitions.
Mbappe also scored the winning goal in Zidane's first match in charge against Turkey in September, although he was forced off shortly afterwards with discomfort in his left knee.
France have collected three wins and a draw from their opening four group matches. Victory over Italy would secure their place in the Nations League quarter-finals.
Real Madrid have made a significant improvement to their injury record under Jose Mourinho, with muscle problems no longer disrupting the squad as frequently as they did last season.
Thomas Tuchel has reaffirmed his commitment to England, insisting he has unfinished business with the national team and intends to remain in charge until at least Euro 2028.
France captain Kylian Mbappe missed training on Wednesday as concerns grow over his fitness ahead of Thursday's Nations League meeting with Italy.
Spain coach Luis de la Fuente is optimistic that Lamine Yamal will recover from a knee injury in time to face England in Sunday's Nations League clash in Madrid.
