Schweinsteiger has suffered a partial tear of the medial collateral ligament in his right knee while training with Germany in the run-up to the friendly with England.
The injury could rule the midfielder out for the rest of the season and Euro 2016.
A statement from the German FA (DFB) read: “The 31-year-old captain suffered a partial tear of the medial collateral ligament in his right knee following a challenge at the end of training on Tuesday afternoon. The diagnosis was confirmed following an MRI scan at the practice of team doctor Dr. Hans-Wilhelm Muller-Wohlfahrt in Munich earlier today.
“He will receive further treatment at his club Manchester United in consultation with the medical department of the national team.”
