The German Football Federation (DBF) said the Brazilian would serve an extra match suspension in addition to the automatic one-game ban for "unsporting behaviour." It means he will not play again in the Bundesliga this season.
A statement on the federation's website (www.dfb.de) was accompanied by a photograph of Rafinha poking his finger in the cheek of Dortmund's Jakub Blaszczykowski immediately after he had been dismissed for elbowing the Pole in the 65th minute.
The incident provoked angry exchanges as Borussia coach Juergen Klopp remonstrated with Rafinha which in turn sparked a protest from Bayern's sporting director Matthias Sammer.
Bayern, who had already won the Bundesliga, meet arch-rivals Dortmund in the Champions League final at Wembley on May 25.