Badstuber, who missed more than half of the current campaign with his first injury sustained in December, will need to undergo surgery again.
"During recovery Holger Badstuber sustained a cruciate ligaments tear and will be out of action for several months," said Bayern, who take on Borussia Dortmund in the Champions League final in London on May 25.
Germany international Badstuber was injured in December after also coming back from a three-week injury break, twisting his knee in their 1-1 draw against Dortmund.
Dortmund's Mats Hummels, meanwhile, will be battling to be fit for the Champions League final against Bayern after limping off in the 2-1 Bundesliga defeat to Hoffenheim in the season finale on Saturday.
"For the Champions League final there are concerns about Hummels," Klopp admitted.
Dortmund, European champions in 1997, take on rivals Bayern in the first all-German final of the competition in London's Wembley stadium on May 25.
They are already racing to get offensive midfielder Mario Goetze - who joins Bayern next season - fit in time for the game with the player recovering from a muscle injury picked up in their semi-final second leg against Real Madrid.