Dembele, who had accepted the charge, will see his suspension extend into next season. Tottenham, second in the Premier League behind newly-crowned champions Leicester City, have two matches remaining.
Television replays appeared to show the Belgian international trying to gouge Chelsea striker Diego Costa's eye during a heated 2-2 league draw at Stamford Bridge on Monday.
That match, which Tottenham had to win to keep their title hopes alive, saw tempers flare after the visitors surrendered a 2-0 lead.
They also became the first team in Premier League history to have nine players booked in one game.
The FA argued the standard punishment of a three-match ban was "clearly insufficient" in Dembele's case, which he contested, and their view was upheld by an Independent Regulatory Commission hearing.
Tottenham's final league games are a home clash with Southampton and an away trip to relegation-threatened Newcastle United.
The Londoners are guaranteed a top-four finish and Champions League qualifying spot but will want to end the season as runners-up ahead of rivals Arsenal who are three points behind.
Dembele has made 29 league appearances this season, scoring three goals.
Tottenham also have England midfielder Dele Alli banned for the rest of the season for violent conduct in an incident also unseen by the referee.
The 20-year-old, voted the PFA Young Player of the Year after a sensational first season in the top flight, was caught on video swinging his arm into the stomach of West Bromwich Albion's Claudio Yacob during a 1-1 draw at White Hart Lane.
(Reporting by Alan Baldwin, editing by Tony Jimenez)
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