The 24-year-old was operated on by renowned knee specialist Dr Richard Steadman in Colorado on Monday.
A club statement said: "Due to extensive ruptures, the player's cruciate ligament is no longer functional and was removed. Before the cruciate can be reconstructed using a surgical tissue graft replacement, the incisions and holes from the original op must heal completely.
"Until then, Holger Badstuber will maintain his physical fitness in sports rehab. The doctors in charge of the case estimate the player will be fit again in around 10 months. The injury is not career-threatening."
Badstuber last week suffered his second cruciate ligament rupture this season, having only returned to training following the initial injury in December.