The defender, who missed most of last season with cruciate ligament damage, has had a meniscus operation on his right knee.
Vidic was left out of United's 2-1 win at Anfield on Sunday, and a subsequent scan brought bad news for the Serbian.
A United club statement said: "Sir Alex (Ferguson), as a precautionary measure, rested Vidic at the weekend, after he complained of tightness in his knee, however, further medical investigation revealed the underlying problem."
It comes as a major blow for United, who are already without England defenders Phil Jones and Chris Smalling.
Vidic is likely to miss Premier League games against Tottenham, Newcastle, Stoke, Chelsea, Arsenal, Aston Villa, Norwich and QPR, plus Champions League matches against Cluj, Braga and Galatasaray.