The Barcelona winger was sent off in the closing minutes of the 4-0 LaLiga win over Sevilla last Monday (AEDT) after confronting referee Antonio Miguel Mateu Lahoz, who had just given debutant Ronald Araujo a red card for a foul on Javier Hernandez.
According to the referee's match report, Dembele said to him, "Very bad, you are very bad", as Barca players surrounded him to argue against Araujo's dismissal.
Barca appealed against Dembele's red card but the RFEF has dismissed their case and given the France international a two-game ban.
He will therefore sit out the trip to Eibar on 20 October (AEDT) and then the visit of Real Madrid to Camp Nou on 26 October.
Araujo has been banned for one game, as has Gerard Pique, who has collected five bookings this season. Both will be available to face Madrid.
Dembele has made three LaLiga appearances this season and scored his first goal of 2019-2020 in the defeat of Sevilla.
Barca is two points behind league leader Real Madrid after eight matches.