The Bantams did not receive written permission for Curtis Good, on loan from the Magpies, 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.
Interestingly, Good was dropped from the squad for today's home game with Torquay as the club await an appeal.