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Ashley Young was injured during Manchester United's 2-1 win over Liverpool on Sunday.
Manchester United maintained their seven-point lead at the top of the Premier League with a 2-1 win over Liverpool, but the victory came at a cost.
Serbian defender Nemanja Vidic, who has only recently returned from a serious knee problem, appeared to suffer the injury after an aerial challenge in the 65th minute of the game but played on until 10 minutes before the end, when he was replaced by Chris Smalling.
Winger Ashley Young, who left Old Trafford on crutches, was hurt in a challenge with Liverpool defender Daniel Agger in the first half and did not return to the field after the interval.
Both Vidic and Young are likely to miss the midweek FA Cup third-round replay against West Ham United and the Premier League trip to Tottenham next weekend.
United defender Jonny Evans was forced to pull out of the game after picking up a hamstring injury following training on Saturday.
The Northern Ireland international is also expected to miss the cup tie against the Hammers.
Striker Wayne Rooney, however, is on the way back to action after recovering from the knee injury he suffered in training on Christmas Day.