The Manchester United midfielder, who damaged the same knee only months ago, has had an injury-plagued first season at the English club, raising concerns about his fitness for the European Championship in France in June.
A medical examination revealed that Schweinsteiger had partially torn knee ligaments.
"This was the result of the medical check today in Munich at the clinic of national team doctor Dr Hans-Wilhelm Mueller-Wohlfahrt," Germany said in a statement on Wednesday.
Germany, World Cup winners in 2014, take on England in Berlin on March 26 and Italy in Munich three days later.
Mesut Ozil and Karim Bellarabi also missed training on Wednesday with minor injuries but coach Joachim Loew said he was confident they would recover in time.
"I expect both of them to be fit for Saturday," Loew said.
The Germans, who have been drawn with Poland, Northern Ireland and Ukraine in Group C, will announce their squad on May 17 but Loew was unsure whether that would also be his final squad.
"I don't know yet. I will have to see how some of the players who are injured come back until then, in what form they are."
Among those missing from the friendly internationals are central defenders Jerome Boateng and Benedikt Hoewedes.
"The battle for the 20-plus-three spots of the squad is already well under way," Loew said. "The young players are really pushing forward."
(Reporting by Karolos Grohmann, editing by Ed Osmond)
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