The 30 year old has recently returned back to the side after missing a large chunk of last season because of a knee injury.
Vidic did not play at the wekend, he was left out of the side by Sir Alex Ferguson as a precautionary measure.
A statement on the club's official website read: "Nemanja Vidic has had a meniscus operation on his right knee and will be out for around eight weeks.
"Sir Alex, 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.
"The central defender was operated on this week and will be sidelined for about eight weeks."