Compliance officer Vincent Lunny imposed the penalty after viewing footage of an incident in Celtic's match at Dundee on Boxing Day.
Wilson tangled with Dundee forward John Baird as the pair raced towards the Celtic penalty area during the first half of the Dens Park clash.
The Englishman admitted catching Baird in the face with his elbow but claimed he was attempting to free himself from his rival, who had hold of his arm.
Baird backed Wilson's view of events, insisting any contact had been accidental.
Celtic manager Neil Lennon said: "Clearly we are very disappointed with today's decision and unfortunately there is no right of appeal.
"We find it disappointing that Kelvin has been found guilty of violent conduct, particularly when the other player has stated it was an accidental incident."
Wilson will miss the home match against Hearts on 19 January and the League Cup semi-final with St Mirren the following weekend.