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.
However, the 25-year-old will not have the chance to feature in the DFB-Pokal showpiece at the Olympiastadion in Berlin.
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."
There had been doubts over the fitness of striker Robert Lewandowski, who is set to play his last game for Dortmund before leaving to join Bayern.
But Klopp is adamant that the 25-year-old will be fit as Dortmund aim to regain the title they won in 2012.
"We have been careful," Klopp added. "As it stands he will train normally today and play tomorrow."
