Deeney grabbed Stoke midfielder Joe Allen's face and neck, with match referee Michael Oliver showing a yellow card to both players.
Stoke manager Mark Hughes described the incident as "unpleasant", saying Deeney should be punished for the incident.
Both clubs have until 1800 GMT on Friday to respond to the charge.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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