Liverpool has also been charged with failing to control its players following the dismissal of midfielder Jay Spearing in the second half.
Pictures in British newspapers appear to show Suarez flashing his middle finger to fans at the end of the match, while Liverpool players surrounded referee Kevin Friend after he showed a red card to Spearing for a challenge on Fulham's Moussa Dembele.
A statement on the FA's website read: "Liverpool Football Club have been charged by the FA with failing to ensure its players conducted themselves in an orderly fashion, following the dismissal of Jay Spearing.
"The charge is in relation to Liverpool's Premier League fixture at Fulham on December 5, 2011. Luis Suarez has also been charged following an incident in the same game. The Liverpool player is charged with improper conduct, in relation to an alleged gesture made towards the Fulham fans at the end of the fixture."
The club has until December 12 to respond to the charges.