The 25-year-old has recently returned after a long-term knee injury, but he had to go off during his side's 2-0 win against Stuttgart this weekend and tests have confirmed that he has torn muscle tendons.
"Of course I'm very disappointed right now," Badstuber told his club's official website.
"But I'm now used to it and I know how to deal with such situations. Don't worry, I will come back and carry on from where I had got back to after my long injury absence. I will not give up."
Badstuber has won 30 caps for Germany since making his debut in 2010.