The incident took place in the 1-1 draw at the Britannia Stadium and Stoke decided not to contest the charge of violent conduct.
The charge was brought based on video evidence after it was not seen by referee Mark Clattenburg or his assistants.
An FA statement confirmed the charge, and said Wilkinson had until 18:00 on Wednesday to respond.
There was more controversy in the fixture when Stoke's Peter Crouch appeared to handball en route to scoring the opening goal.
- Mark Clattenburg