Outspoken Mourinho made the gesture during last weekend's home clash against Sampdoria, which the league leaders drew 0-0 despite having defenders Walter Samuel and Ivan Cordoba sent off in the first half.
Mourinho's ban starts with Sunday's match at Udinese.
Argentine midfielder Esteban Cambiasso also had his appeal against a two-match suspension for trying to punch an opposition player in the tunnel at halftime turned down, the FIGC said on its website.
But Sulley Muntari had a two-match ban for swearing at an official halved.
Inter, whose lead over second-placed AC Milan has been cut to four points following three straight draws, will be without several players at Udinese. Samuel and Cordoba are also suspended after their red cards.
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