The incident happened during the 1-1 draw between the two sides at the Britannia Stadium at the weekend, in which Peter Crouch's opener was cancelled out by a debut goal from Javi Garcia.
Referee Mark Clattenburg and his team of officials failed to spot the incident, prompting the FA to retrospectively charge the defender.
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Wilkinson, 28, has made 135 appearances for the club and has previously played for Shrewsbury Town and Blackpool on loan.
He now has until 18:00BST on Wednesday to respond to the charge and, if found guilty, could miss three Potters matches, starting with their trip to face Chelsea in the Premier League at the weekend.