Michael Duff's side will face the Sky Bet League Two outfit at Oakwell in the Emirates FA Cup second round.
The Reds progressed to this stage of the competition after beating Bolton Wanderers 2-1 in Greater Manchester last Saturday.
The Alex overcame Leyton Orient in the first round by one goal to nil courtesy of a Bassala Sambou strike in added time at The Mornflake Stadium.
The second round tie is set to be played on the weekend of 26 November.
Ticket details regarding the fixture will be released in due course.
