Khedira was forced off during Germany's 1-1 draw with Italy on Friday, and now scans have confirmed the extent of the damage.
Germany team doctor Hans-Wilhelm Muller-Wohlfahrt has revealed that surgery is required, but they hope he will be back in time for next summer's World Cup finals.
"Sami has to be treated surgically, we hope that he will be healthy again for the start of World Cup," said Muller-Wohlfahrt.
Germany coach Joachim Low added: "This is a bitter blow for Sami and all of us.
"He is a great player on and off the pitch, he is always thinking positively and this will help and I am optimistic that he will be back in time for the kick-off of the World Cup.
"We wish him all the best and keep our fingers crossed that the surgery goes well and he can quickly get into rehab."
Low also revealed that star trio Philipp Lahm, Manuel Neuer and Mesut Ozil would be rested for the England game on Tuesday.
He added: "The game against England is for us the last chance before the World Cup to test different tactics and players.
"Philipp Lahm, Manuel Neuer and Mesut Ozil are key and for me it's more important now to see other players in those key positions just to give a chance to prove themselves against a great team like England."