Khedira, 26, was substituted during the second half of the international friendly in Milan after landing awkwardly on his right knee.
It has since been confirmed that his right anterior cruciate ligament was torn, and that he will undergo surgery before beginning a six-month rehabilitation programme.
“Sami will have to be treated surgically,” Germany team doctor Hans-Wilhelm Muller-Wohlfarth said.
“He will need to be operated on but we are hopeful he could be fit in time for the World Cup.”
Khedira now faces a race against time to be fit for Germany’s World Cup campaign in Brazil. Such injuries usually take at least eight months from which to recover, and often a player will not be fully fit for around a year.
"This is a bitter setback for Sami. But he always thinks positively and that is why I am optimistic he will be ready and fit when the World Cup starts," coach Joachim Loew said.
Germany face England in a friendly at Wembley on Tuesday night, with big-name trio Mesut Ozil, Manuel Neuer and Philipp Lahm all omitted from the squad as Loew seeks to test out his squad.