The tie will be played on Sunday 2nd December with kick off at 2pm and the match has been selected for live BBC Final Score coverage.
Ticket prices will be confirmed and go on sale in due course.
It is the only game in the Second Round where two non-league sides face each other and both teams caused upsets in the previous round.
The Bees defeated League One side Bristol Rovers after a replay whereas Stockport went to Huish Park and knocked out League Two side Yeovil Town.
Barnet’s home league fixture against Chesterfield that was scheduled for December 1st has now been postponed and a new date will be arranged.
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