The Paris St Germain winger was called into the squad to face Uruguay and Brazil last week but has not featured for PSG since their match against Lyon on 12 May.
And, after discussions between France manager Didier Deschamps and the medical team at the newly-crowned French champions, it has been decided the 26-year-old will not feature in the upcoming matches.
A statement from the FFF said: "Didier Deschamps endorsed this package after an exchange between the medical staff of the Paris Club and the team doctor of France, Franck Le Gall."
Lyon forward Alexandre Lacazette will take Menez's place after an impressive season for Remi Garde's men.
The 21-year-old, who has scored four goals for Lyon this season, has featured at every age group from U-16 to U-21 for France and could be in line for a senior debut.
Deschamps' men take on Uruguay in Montevideo on June 5 and Brazil in Porto Alegre four days later.