The Northern Irishman is said to have confronted a match official as the players left the field at Villa Park, following a 2-0 victory for the hosts.
An FA statement read: "It is alleged that in or around the tunnel area after the end of the fixture the player used abusive and/or insulting words and/or behaviour towards a Match Official."
The last-eight tie – settled by goals from Fabian Delph and Scott Sinclair - was overshadowed by a pitch invasion that saw thousands of fans spill onto the field at full-time.
A number of supporters had earlier entered the field of play following Sinclair's 85th-minute effort and during stoppage time.
The FA are currently investigating those incidents, while Brunt has been given until Thursday to respond.
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