The Bantams did not receive written permission for Curtis Good, on loan from Newcastle, to play in the competition by the 12pm deadline on the day of the fixture, which ended 1-1 at Valley Parade.
The decision is subject to an appeal, which if unsuccessful would see Brentford progress to the third round to play Bury or Southend.
An FA statement read: "The FA has confirmed that Bradford City have been removed from The FA Cup with Budweiser 2012-13 competition after fielding an ineligible player in their Second Round tie against Brentford.
"Bradford City did not have the necessary written permission for Curtis Good to play in the competition, while on loan from Newcastle United, by the 12pm deadline on Friday 30 November prior to the fixture that evening.
"Bradford's removal from the competition is subject to appeal, but if this appeal is unsuccessful Brentford will go forward to the Third Round and play either Bury or Southend United."
Bradford admitted the error was "of an administrative technical nature" and have apologised to their fans.
City were the only side left in three domestic cup competitions and face Premier League giants Arsenal in the quarter finals of the Capital One Cup on Tuesday December 11.
A Bradford statement read: "Bradford City Football Club were charged by the FA of rule 15 (j) (i) on Monday 3 December 2012 in relation to their FA Cup with Budweiser Second Round encounter with Brentford on the 30 November 2012.
"The nature of the charge is the playing of one of our loan players deemed ineligible due to the late submission for permission for him to play. Bradford City Football Club is very sorry to have to report such a matter and apologies 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 6 December, 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 and cannot comment further on this matter as the club is still actively conducting a full investigation. The club has until 5:00pm today (Friday) to lodge an appeal with the FA and we are currently reviewing our position in relation to this."
Brentford chief executive Mark Devlin admitted he had sympathy with Bradford and would have preferred to have advanced in the competition another way.
He told Sky Sports News: "It is not a satisfactory way to progress, we would much rather prefer to progress by winning a match but the FA have made their decision and that's it really.
"The first we heard of anything was on Monday afternoon and internally we just held off before putting tickets out for sale for the replay and just waited for the FA's decision from yesterday's committee hearing.
"It is the FA's competition, the FA make the rules which we all know about. Whether we feel sympathetic or not does not come into play really. It is the FA's decision. I do have some sympathies with Bradford.
"It is entirely a matter for the FA and Bradford City Football Club. I don't think we will be asked to get involved any further at this stage."