His club, Liverpool, have also been fined £20,000 for failing to control their players in the same match. Suarez will now miss Friday's game at home to Newcastle.
The rulings, announced today by the FA, come at a sensitive time for the Reds, who have made clear their anger over an eight-game suspension handed to the Uruguayan striker for racially abusing Manchester United's Patrice Evra.
The Fulham match, on 5 December, saw the Liverpool midfielder Jay Spearing sent off, which led to a group of Liverpool players remonstrating with the referee, Keith Friend.
The club admitted the charge of failing to ensure their players conducted themselves in an orderly fashion but contested the financial penalty. Despite Liverpool contesting the fine, an independent regulatory commission ruled it was applicable.
Both the club and Suárez, who was pictured apparently giving supporters a one-fingered gesture and admitted the charge against him, have been warned about their future conduct.
Liverpool, whose players and manager, Kenny Dalglish, wore Suárez T-shirts in the warm-up of their match against Wigan, look certain to appeal the eight-game ban once they have assessed the commission's detailed report. Liverpool said they had no comment to make on either Suarez's ban or the imposition of a fine on the club.