The Olympique Lyonnais star will miss les Bleus' World Cup qualifiers in September, while Didier Deschamps had words of warning for Franck Ribery
The Olympique Lyonnais midfielder, 22, suffered the injury during his side's Champions League play-off defeat to Real Sociedad in August and sat out Saturday's defeat to Evian in Ligue 1 as a result.
In a statement on their website, the French Football Federation confirmed that Grenier had "not recovered enough" from the injury and will miss the World Cup qualifiers against Georgia and Belarus on Friday and Tuesday respectively.
France are a place and a point behind leaders Spain in Group I and will face the group's bottom two sides in the next seven days.
Franck Ribery is likely to feature against Georgia for his first international appearance since winning Uefa's Best Player in Europe award, though head coach Didier Deschamps warned the winger to cut down overcomplicating his football.
"When he's playing for his country he really gives his best and tries to be decisive and make the rest of the team give their best," he said.
"Sometimes he can play too complicated trying to make the difference. He just needs to find the good balance.
"At Bayern Munich he's been doing well for a while now. We can be proud of what he is achieving. He's a French player and the best European one."