Barnet will now face Aldershot Town at The Hive on Tuesday 21st January 2014 at 7.45pm.
The Bees had been due to face the Shots on Saturday 14th December but that fixture is not able to take place due their progression in the FA Trophy.
Edgar Davids’ side will instead face Grimsby Town on the 14th after they overcame Coalville Town with a 3-0 win on Tuesday in a first-round replay.
Revenge will also be on the cards for the Bees who were beaten 2-1 by the Mariners at Blundell Park last month.
Ticket news for the FA Trophy second round tie will be released shortly.