Higuain was shown his second yellow card for kicking out at defender Felipe, prompting the striker to launch a verbal tirade against the referee. The 28-year-old had to be pulled away by team-mates as he tried to angrily remonstrate with Udinese players.
Higuain, the top Serie A scorer with 30 goals, is set to miss upcoming games against Verona, Inter Milan, Bologna and Roma, severely damaging his side's chances of a first Serie A title in 26 years.
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However, Napoli said on Tuesday night that they would appeal, describing the ban as "unfair and excessive".
Defeat left Napoli six points adrift of leaders Juventus, as they bid to snatch a first league title since Diego Maradona played his penultimate season at the club in 1990, with seven games to play.
The disciplinary commission sanctioned "an insulting term" used against the referee as well as "a disrespectful gesture when he faced him and laid his two hands on his chest".
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It also evoked "aggressive behaviour towards an opponent" and pointed out that Higuain had "to be restrained by his teammates".
Napoli, who are second with Roma four points behind, are already weakened for their next game at Verona following suspensions of defender Kalidou Koulibaly and striker Dries Mertens.
Napoli coach Maurizio Sarri will also be suspended for a match after he was sent to the stands for dissent during the game.
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