The Australia international has played in three of Dortmund's five games in the competition this season, although he did not feature in the quarter-final with Eintracht Frankfurt or the semi-final against Wolfsburg.
Langerak has been named in Australia's provisional squad for the FIFA World Cup and is in contention to start for his country at the tournament in Brazil next month.
Regular goalkeeper Roman Weidenfeller is expected to start, while Zlatan Alomerovic will deputise for Langerak on the bench.
"His knee has been slightly overstretched," Dortmund coach Jurgen Klopp said.
"There is a slight stretch. In the period from Tuesday evening until today (Friday) it has not been possible to get him fit for the final.
"He won't need an operation. He will be out for two weeks."
"We have been careful," Klopp added. "As it stands he will train normally today and play tomorrow."
