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Uefa’s disciplinary panel deemed that the centre-back was guilty of violent conduct for striking his knee into the back of Barca forward Alexis Sanchez in the game at Camp Nou in April.
Terry has already served a mandatory one-match ban in sitting out the Blues' victory over Bayern Munich at the Allianz Arena in this season’s final.
Consequently, the former England skipper will be ineligible for selection for the Super Cup match against Europa League winners Atletico Madrid, which will be played in Monaco in August.
He will also miss Chelsea’s first Champions League fixture next season after they qualified, despite missing out on a top-four finish, by virtue of winning the competition.
Terry, who is currently preparing for Euro 2012 with the England squad, has the option of fighting the suspension at Uefa’s appeals panel.