The Bees entered the draw in the first round, while The Blues beat AFC Dunstable 2-0 in the final qualifying round.
Last season saw Barnet lose in the first round 3-1 at home to Luton, meanwhile, Wingate & Finchley lost 3-2 in extra time against Beaconsfield SYCOB in the second qualifying round.
The tie has to be played by the 4th November, the club will release the date of the fixture once it’s been finalised.
