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
EURO 2012
Group A
Poland
Greece
Russia
Czech Republic
Group B
Holland
Denmark
Germany
Portugal
Group C
Spain
Italy
Republic of Ireland
Croatia
Group D
Ukraine
Sweden
France
England
EURO 2012 FINALS MATCH SCHEDULE
All match kick-off times are BST.
GROUP STAGES
Friday June 8
Warsaw, Group A: Poland v Greece (1700)
Wroclaw, Group A: Russia v Czech Republic (1945)
Saturday June 9
Kharkiv, Group B: Holland v Denmark (1700)
Lviv, Group B: Germany v Portugal (1945)
Sunday June 10
Gdansk, Group C: Spain v Italy (1700)
Poznan, Group C: Republic of Ireland v Croatia (1945)
Monday June 11
Donetsk, Group D: France v England (1700)
Kiev, Group D: Ukraine v Sweden (1945)
Tuesday June 12
Wroclaw, Group A: Greece v Czech Republic (1700)
Warsaw, Group A: Poland v Russia (1945)
Wednesday June 13
Lviv, Group B: Denmark v Portugal (1700)
Kharkiv, Group B: Holland v Germany (1945)
Thursday June 14
Poznan, Group C: Italy v Croatia (1700)
Gdansk, Group C: Spain v Republic of Ireland (1945)
Friday June 15
Donetsk, Group D: Ukraine v France (1700)
Kiev, Group D: Sweden v England (1945)
Saturday June 16
Wroclaw, Group A: Czech Republic v Poland (1945)
Warsaw, Group A: Greece v Russia (1945)
Sunday June 17
Kharkiv, Group B: Portugal v Holland (1945)
Lviv, Group B: Denmark v Germany (1945)
Monday June 18
Gdansk, Group C: Croatia v Spain (1945)
Poznan, Group C: Italy v Republic of Ireland (1945)
Tuesday June 19
Donetsk, Group D: England v Ukraine (1945)
Kiev, Group D: Sweden v France (1945)
QUARTER-FINALS
Thursday June 21
Warsaw, QF1: Winner A v Runner-up B (1945)
Friday June 22
Gdansk, QF2: Winner B v Runner-up A (1945)
Saturday June 23
Donetsk, QF3: Winner C v Runner-up D (1945)
Sunday June 24
Kiev, QF4: Winner D v Runner-up C (1945)
SEMI-FINALS
Wednesday June 27
Donetsk, SF1: Winner QF1 v Winner QF3 (1945)
Thursday June 28
Warsaw, SF2: Winner QF2 v Winner QF4 (1945)
FINAL
Sunday July 1
Kiev: Winner SF1 v Winner SF2 (1945)