Dembele was sent off near the end of Barca's 4-0 win over Sevilla on Sunday for saying to referee Mateu Lahoz: "very bad, very bad".
The RFEF disciplinary committee ruled that Dembele's reaction constituted an "attitude of contempt or disregard for referees" and suspended the Frenchman for two matches.
It means Dembele is unavailable for Barca's upcoming La Liga fixtures away at Eibar on October 19 and at home to Real Madrid on October 26.
Madrid and Barca are first and second in the table after eight games.
Ronald Araujo, a 20-year-old defender, and Gerard Pique both received one-match bans and will also miss the game against Eibar.
"FC Barcelona has decided to appeal the sanctions imposed by the disciplinary committee to both Ousmane Dembele and Ronald Araujo," the club said in a statement.
Pique picked up his fifth yellow card of the season against Sevilla while Araujo was sent off for bringing down Javier Hernandez when the striker was through on goal.