Vidic was rested for the 2-1 weekend win at Liverpool after complaining of tightness in his right knee, but further tests revealed the true extent of the problem, and the Serb has since had a meniscus operation.
"Nemanja Vidic has had a meniscus operation on his right knee and will be out for around eight weeks," a club statement read.
"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. The central defender was operated on this week and will be sidelined for about eight weeks."
The 30-year-old, who is United's captain, missed the final five months of last season after rupturing cruciate knee ligaments in a UEFA Champions League defeat to Basel in Switzerland.