The 27-year-old Serb sustained the injury during the warm-up ahead of a friendly against Bayern Munich, and has been ruled out of the Community Shield against Chelsea this Sunday.
And manager Sir Alex Ferguson also confirmed that the injury will cause him to miss the club's Premier League opener against Birmingham City.
Vidic, who will be out of action for up to two weeks, joins Gary Neville, Wes Brown and goalkeeper Edwin Van der Sar on the treatment table.
"Everyone is fit apart from Wes, Vidic and Neville," Ferguson was quoted as saying on the club's official website.
Brown and Neville have been have been ruled out of Sunday's match with thigh and groin strains respectively while Van der Sar faces an eight-week layoff with a broken finger.
"Vidic has pulled his calf and is another week or two away, while Edwin's injury is a bad one. He's out for 8-10 weeks, of course.
"So my first selection dilemma for Sunday is in goal. It is not an easy one for me," Ferguson added.
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