City secured a 3-1 victory in their first round tie at Scunthorpe's Glanford Park thanks to an opener from Joe Brennan and a second half double by Callum Chippendale.
Barnsley booked their date with the Bantams by defeating Carlisle United 2-1 at Brunton Park on the same night.
Although no date has been confirmed for the tie as of yet, the second round match must be played by Saturday 22 November 2014. The tie will also take place at the Coral Windows Stadium.
The draw for the third round, when Premier League and Championship sides enter the competition, will be made on Friday 7 November 2014.