The Australian midfielder received a straight red card at the full-time whistle after appearing to get involved in a confrontation with Newcastle's Yohan Cabaye.
The Frenchman has since apologised for his role in the skirmish and the Football Association will now review the incident.
Cahill may miss Everton's first three games of the 2012/13 season should the appeal prove unsuccessful.
Cabaye: "I would like to apologise for the cross words I exchanged with Tim Cahill which resulted in his red card and my booking on the final whistle.
"It was unnecessary and, regrettably, the result of frustration and disappointment, all in the heat of the moment. It is out of character and for that I am sorry."
FOLLOW EURO 2012 WITH NEWCASTLEUTD-MAD
Source: FOOTYMAD
