The 26-year-old picked up the injury in Germany's 1-1 draw with Italy on Friday after a collision with Azzurristar Andrea Pirlo and was promptly forced to leave the pitch after 67 minutes.
Khedira visited the hospital for further examination and a series of tests have now revealed that he has suffered a torn ACL.
"Sami will have to undergo surgery. We hope that he will be healthy again at the start of the World Cup," Germany doctor Hans-Wilhelm Muller-Wohlfahrt told the official DFB website.
No exact details have been given about the length of Khedira's absence, but the midfielder is expected to be out of action for at least six months.
"This is a huge blow for Sami and the rest of the team. He's a real fighter, though, and always remains optimistic. That will help him," Germany coach Joachim Low commented.
"I am optimistic that he will be ready in time for the World Cup in Brazil."