The defender's elbow on the Italian striker was missed by referee Mark Clattenburg last Saturday, but the FA have now taken retrospective action and punished the offence
The 28-year-old struck the Italian as the ball went out for a throw-in, an incident which was missed by the match officials but not the FA's Disciplinary Panel, who charged the Potters defender with violent conduct.
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Wilkinson has decided not to contend the punishment, and will serve his ban with immediate effect, starting with his side's trip to Chelsea on Saturday.
He will also miss the visit of Swansea, as well as Stoke's trip to Anfield in three weeks time.
Manager Tony Pulis had previously confirmed that the club would not appeal the decision, after reviewing footage of the incident.
"We've had a look at the video but will have to take it on the chin," he told the Daily Telegraph.