Effenberg captained Bayern the last time they won the competition in 2001, and he has called on Schweinsteiger to rise to the occasion at the Allianz Arena.
"There is a lot of hope resting on his shoulders and he cannot buy any more time - he has got to work now," Effenberg told the Bild newspaper.
"Sooner or later, he has got to be there to lead this team. I am keen to see whether he can cope with the pace. He has got to play intelligently."
Effenberg claimed Jupp Heynckes's side, who were beaten to the Bundesliga title and DFB-Pokal by Borussia Dortmund, are too reliant on wingers Franck Ribery and Arjen Robben and are "too predictable".
"It is not good when you are always hoping that Ribery and Robben won't get stopped," he added.
"Given the quality Bayern have, they have got to be able to play other systems too. They are too predictable. A win in this game would save their season."