The Liverpool forward has been barred from all football-related activity for four months, banned for nine competitive international matches and hit with an €80,000 [£64,000] fine.
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Jose Murjica, the president of the Uruguay FA, however, has criticised the ban, calling it "fascist".
"Fifa are a bunch of old sons of bitches,” he said, speaking to a journalist. “They could have punished him, but not given him this fascist ban.”
The 79-year-old echoes the sentiments of his compatriots, including national captain Diego Lugano, who have largely refused to accept Suarez’s sanctions.
Suarez was previously banned for seven matches in 2010 for biting PSV's Otman Bakkal, during his time at Ajax.
Most recently, he was suspended for a further 10 games after biting Branislav Ivanovic of Chelsea while playing for Liverpool in the Premier League.
The Uruguayan FA have informed Fifa that they will appeal against the ban, while Suarez himself has argued that he lost his balance, making his face collide with Chiellini’s shoulder.