Dunk was wrongfully sent off on the weekend after he was booked twice against Bournemouth.
However, Mike Dean thought Dunk had fouled David Brooks, however, it was his teammate Yves Bissouma.
Dean was left with no choice but to give the Brighton man his marching orders 15 minutes from time when after a foul to Junior Stanislas.
When players are wrongfully dismissed clubs can appeal the ban – however, that only applies after a straight red card.
Because Dunk was sent off after two bookings Brighton will not be able to appeal the decision leaving them without their star defender for the Boxing Day clash at home to Arsenal.
The law states: "A claim of wrongful dismissal may be lodged only for on-field offences which result in a sending off, except for two cautions leading to a dismissal."
Arsenal come into the game off the back of a 3-1 win at home to Burnley with top scorer Pierre-Emerick Aubameyang netting twice.
The Gunners had come into the game on a two game losing streak with defeats to Southampton and Tottenham.
Brighton come into the game having lost three straight with defeats to Burnley, Chelsea and Bournemouth.
Their last win came against rivals Crystal Palace earlier in the month when they triumphed 3-1 at home.
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