Khedira came off midway through the second half of the 1-1 draw with the Italians in Milan, and the German Football Federation (DFB) confirmed on Saturday that the 26-year-old had suffered a ruptured anterior cruciate ligament in his right knee.
"We hope that he will recover before the 2014 World Cup," the DFB said, without confirming exactly how long he will be unavailable.
It is a major blow both for Germany and for Khedira's club Real Madrid, where he is a regular starter in Carlo Ancelotti's side.
"It is a big blow for Sami and for all of us. But he is a fighter both on and off the pitch and he always thinks positively," said Germany coach Joachim Low. "I am optimistic and I hope he will be back in time for the World Cup."
Depending on the gravity of the injury and whether or not it needs surgery, it typically takes a minimum of four months and sometimes up to eight months to recover from a torn cruciate knee ligament.