The Bantams did not have written permission to field on-loan Newcastle defender Curtis Good in their second round clash against Brentford, which ended 1-1.
Should the appeal fail, Brentford will automatically progress to the third round where they will face the winner of the replay between Bury and Southend United.
A statement on the club's website read: "Bradford City Football Club can confirm that they will be appealing The FA's decision to expel the club from this season's FA Cup competition.
An earlier statement read: "Bradford City Football Club is very sorry to have to report such a matter and apologises to our fans. The error was of an administrative technical nature and not one to intentionally break competition rules.
"We presented a case of mitigation to the FA on Thursday, however the FA panel chose to enforce the full powers of its jurisdiction and have removed the club from the FA Cup competition.
"We are clearly disappointed by this decision."