Terry sat out Chelsea's victory over Bayern Munich in the final to serve a mandatory one-match ban.
But UEFA's disciplinary panel has added two more games, after ruling that Terry was guilty of violent conduct when he struck his knee into the back of Barcelona forward Alexis Sanchez during the second leg of the semi-final at Camp Nou.
The centre-back is now ineligible for the Super Cup match against Europa League winners Atletico Madrid in August as well Chelsea's first Champions League group-stage game in September.
Terry and Chelsea can challenge the sanction at UEFA's appeals panel.
The Blues skipper was still allowed to lift the trophy at the Allianz Arena after a penalty shoot-out success against Bayern ended the club's wait for Europe's most coveted trophy.
