The quartet are all being investigated for separate Euro 2012 incidents, with Manchester City star Nasri in hot water for verbally abusing a French journalist following their 2-0 quarter-final defeat to Spain.
Paris Saint-Germain winger Menez is believed to have insulted his captain Hugo Lloris after the same game.
Ben Arfa and M'Vila, meanwhile, are both in trouble following bust-ups with coach Laurent Blanc.
Newcastle star Ben Arfa was involved in a dressing room spat with Blanc while M'Vila refused to shake his hand when he was substituted.
The FFF confirmed that the four players' bonus money of 100,000 euros for reaching the Euro 2012 quarter-finals has been frozen pending the disciplinary proceedings.
"Hatem Ben Arfa, Yann M'Vila, Samir Nasri and Jeremy Menez are summoned to appear before the disciplinary committee," said FFF president Noel Le Graet.
Coach Blanc left his post following the troubled tournament after deciding against renewing his contract.
Former Chelsea midfielder Didier Deschamps, who has just quit his job as Marseille boss, has been heavily tipped to replace him.
Le Graet revealed that the 43-year-old has asked for more time to consider whether to take the position.
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