Manchester City midfielder Nasri has been banned for three matches after an expletive-laden rant at reporters following France's quarter-final defeat by Spain, the French Football Federation (FFF) confirmed this afternoon.
Paris St Germain winger Menez, who was not present at the hearing, will sit out one game as punishment for confrontations with both Italian referee Nicola Rizzoli and his own keeper Hugo Lloris during the last-eight clash.
The other two players up in front of the commissiion, Yann M'Vila and Hatem Ben Arfa, escaped with warnings.
Rennes midfielder M'Vila's charge also stemmed from the Spain match, when he was substituted and did not shake hands with either his replacement Olivier Giroud or coach Laurent Blanc.
Newcastle playmaker Ben Arfa, meanwhile, was referred to the commission over an alleged argument with Blanc in the dressing room after the group-stage defeat to Sweden.
As a result of the sanctions, Les Bleus' new coach Didier Deschamps will be without both Nasri and Menez for their August 15 friendly against Uruguay.
Nasri will also be sidelined for their first two qualifying matches for the 2014 World Cup, away to Finland on September 7 and at home to Belarus four days later.
The FFF announced the decisions in a press release which added that the verdicts will be passed on to their executive committee, who have the right to retain the players' appearance bonuses in part or in full.
The players reported to the FFF's headquarters in Paris today with the exception of Menez, who is on Paris St Germain's pre-season American tour.
The 25-year-old was represented by his lawyer Carlos Alberto Brusa, who told l'Equipe: "He (Menez) regrets what happened and wants to put this difficult time behind him. It was a youthful error.
"He is not there, I am there to represent him and pass on his message.
"It is a big responsibility, in front of the commission, to represent a player and to tell his story."
FFF discipline commission president Jean Mazzella told L'Equipe: "The meeting was calm, the players gave explanations and showed a very good attitude.
"They defended themselves but they answered all the questions we asked them. They did not apologise, they showed regret."