The Catalan giants threw away the chance to move top after a shock 2-1 loss at the Camp Nou on Thursday evening.
Koeman was sent to the stands midway through second half, and he will now miss the upcoming against Valencia and Atletico Madrid.
After the game, the Dutchman insists he was baffled about why he was sent off by the referee.
"I don't get it at all. I didn't say anything, I didn't insult him. I spoke to the fourth referee and he disrespected me," Koeman said after the game.
"I was not wrong, because according to the referee report I disrespected the fourth referee and for me, it is not like that.
"A lack of respect is insulting. I haven't used ugly words, not once. If they're going to put things I haven't said I'll have to do something. I don't understand."
The Catalan giants have already confirmed their plans to appeal Koeman's suspension.
"FC Barcelona will present an appeal against the suspension given to Ronald Koeman," a statement from the club read.
"The RFEF Competition Committee announced this Friday that the red card received by the coach in the LaLiga game against Granada at the Camp Nou has resulted in a two-game touchline ban."
