The former England captain is understood to have suffered the injury during training on Friday. United manager Sir Alex Ferguson is already stretched in defence for the trip to Goodison Park, as he is without Chris Smalling, Phil Jones and Jonny Evans.
It means that Michael Carrick is in line to play at centre-back alongside Nemanja Vidic, who will be making his first competitive appearance for United since suffering a cruciate knee ligament injury against FC Basel in the Champions League last December.