FIFA's disciplinary panel imposed the ban on June 26.
In his submission to that hearing, Suarez wrote that he did not deliberately bite Chiellini, but had lost balance and fell with his mouth open on the Italian's shoulder.
Suarez later apologized, and Chiellini accepted.
The ban currently expires on Oct. 25, the same weekend that Barcelona is due to visit Real Madrid in the first "clasico" of the season.
Because Suarez is barred from all "football-related activity," he cannot train with his new club, which he joined from Liverpool this month.
If Suarez loses his appeal, he will also miss three Champions League group matches.
Uruguay's next competitive match is at the Copa America, which kicks off in June 2015 in Chile.