The FFF held a hearing on Friday and decided that the Manchester City midfielder must serve a three-match suspension due to the foul-mouthed insults he directed at reporters following France’s quarter-final defeat to Spain.
Paris St Germain winger Jeremy Menez also faces a one-game ban for his behaviour in relation to an argument with the referee during the Spain game as well as a row with captain Hugo Lloris.
Two other France players, Yann M’Vila and Hatem Ben Arfa escaped with a warning following their hearings.
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 then 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.
The clampdown on the behaviour of France players comes as a result of the 2010 World Cup debacle that saw several of the squad propose strike action during the tournament in South Africa.
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.”
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.