Appealing to CAS in such circumstances is highly unusual but Bayern described the ruling as harsh and said Ribery was disappointed and sad to be missing the final against Inter Milan.
The French playmaker, who has already served one match of the ban, was dismissed before half time in the first leg of the semi-final against Olympique Lyon for a studs-up challenge on Lisandro Lopez.
"We will keep on fighting," Bayern chairman Karl-Heinz Rummenigge told reporters. "We're not happy with the decision here and we will take the decision to CAS in Lausanne.
"For him to miss the Champions League final for an offence of foul play is just too harsh," he added.
"Foul play should be punished with a one-match ban, those are the UEFA statutes but they have not followed them," added Rummenigge. "It's much too harsh."
"Given the outcome of the proceedings, Bayern Munich and the player have the right to lodge an appeal at the Court of Arbitration for Sport," UEFA said.
World football's governing body's statutes differ from UEFA's and only allow an appeal when a player is banned for four games or over, or a minimum three-month period.
Ribery's lawyer has said her client was only questioned about his ties with the leader of an escort girl network and the player has made no comment about the affair.
