Nasri banned over behaviour at Euro 2012
The 25-year-old Manchester City player swore at a reporter following the quarter-final loss to Spain and made a gesture after scoring against England.
Jeremy Menez of Paris Saint-Germain was also given a one-match ban after he argued with goalkeeper Hugo Lloris during the Spain match.
Both players will miss a friendly against Uruguay next month and Nasri will also sit out 2014 World Cup qualifiers against Finland and Belarus.
Midfielders Hatem Ben Arfa and Yann Mvila were given warnings following separate incidents during the tournament.