The winner of next week's FA Cup first-round replay between the Blues and Oldham will face League Two Barrow at home in round two.
Town and the Latics are set to meet at Boundary Park on a day yet to be confirmed but probably Tuesday.
Barrow are currently 15th in League Two and won 4-0 at Banbury in round one.
Town and the Bluebirds, who returned to the EFL after an absence of 48 years in 2020/21, have never previously met in any competition.