Dembele came on as a substitute in second-half during his team’s 1-1 draw with Hungary on Saturday but had to be replaced after 30 minutes.
“Ousmane Dembele had an X-ray at the Budapest hospital on Sunday night,” the French Football Federation said in a statement on Monday.
“The recovery time is incompatible with him staying in the squad.”
World champions France play holders Portugal in their final group game on Wednesday.
Didier Deschamps’ side lead Group F on four points after two games, one ahead of second-placed Germany and third-placed Portugal.
Deschamps still has other attacking options behind starters Antoine Griezmann, Karim Benzema and Kylian Mbappe, with Olivier Giroud, Kingsley Coman and Wissam Ben Yedder in the squad.
