Brazil are currently preparing to host the Confederations Cup and the Bayern pair were part of Luiz Felipe Scolari's squad for the event.
They claim FIFA rules impose a deadline on the squad being together for this coming Saturday, the day Bayern are due to face Stuttgart in their last game of the season in Berlin.
Were the pair to feature in that game, they would miss the deadline and not be able to take part in the competition, and Bayern have reluctantly agreed to release them.
"If we didn't release them, then Brazil would report us to FIFA and the punishment could lead to us losing the DFB-Pokal final 2-0, even if we were to win it," said Bayern's chairman Karl-Heinz Rummenigge.
"We are going to release them. They are going to fly to Rio today via Frankfurt."
Rummenigge has blamed the German Football Association (DFB) for scheduling the final so late, and the Brazilian FA for influencing the players.
"I find it unethical and inhumane the pressure which has been placed on the players," Rummenigge said in Munich today, according to sport1.de.
"You get the impression that a psychological war has been waged on them both, as if their international careers would be over if they did not travel."
The Bayern pair, fresh from winning the Bundesliga and the Champions League, will therefore be available for selection in Brazil's friendly match with England on Sunday, although they will be deprived of the chance to win the treble with their club.