The in-form Germany international, who has scored seven league goals and set up another five this season, underwent tests on Sunday morning after picking up the injury early in the game.
"His absence is very bad news for us," said Leverkusen sports director Rudi Voller. "This is the game of games for us in the Champions League so we have to put everything we have in it even without Sam."
Leverkusen, second in the Bundesliga, are also second in their Champions League group, a point behind leaders United, who have eight. Ukraine's Shakhtar Donetsk, in third, have five points while Real Sociedad are bottom on one.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
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