Schweinsteiger picked up the problem during the Red Devil's 1-0 FA Cup win over Sheffield United on Saturday.
And the Germany international becomes the fifth player unavailable to United boss Louis van Gaal.
Antonio Valencia (foot), Luke Shaw (leg) and Marcos Rojo (shoulder) are already out while Phil Jones is unlikely to feature because of his ankle problem.
REUTERS
Bastian Schweinsteiger suffered a knee injury against Sheffield United
However, Ashley Young, Michael Carrick and Morgan Schneiderlin are likely to return to the squad after being rested for the 1-0 win over the Blades.
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