The Borussia Dortmund star suffered a partial ligament tear in his country's 6-1 friendly victory over Armenia on Friday.
Centre-back Shkodan Mustafi has been called up as his replacement for the tournament, which kicks off in Brazil on 12 June.
Germany coach Joachim Low said: "It is extremely regrettable for him and for us.
"Marco was in excellent shape.
"He was superb in our training camp and during our friendlies against Cameroon and Armenia. He showed a real joy for playing. We all expected him to play a major role in this competition."