The 32-year-old's ban has been upheld after he was given a straight red card for his challenge on Eden Hazard during Manchester United's 3-1 defeat to Chelsea on Sunday
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United manager David Moyes stated after the match that he did not think Vidic should have been dismissed for his challenge on the Chelsea midfielder.
"Vidic's for me is not a red card, it was a yellow card," said the Scot.
Vidic will now miss Wednesday's Capital One Cup semi-final second leg against Sunderland, as well as Premier League fixtures against Cardiff City and Stoke City.
The Serb will next be available for selection on February 9 as United host Fulham at Old Trafford.
Defeat for David Moyes' side on Sunday has left the Premier League champions seventh in the table, 14 points behind leaders Arsenal and six points adrift of the Champions League places.