Town have been drawn away against League Two AFC Wimbledon or Isthmian League South East Division Ramsgate in the third round of the FA Cup.
The Dons, who are 10th in the fourth tier, host the Kent side, who are top of the eighth, at Plough Lane in their second round tie live on ITV4 on Monday at 7.45pm.
Town have never previously met either club in the FA Cup. Former Blues forward Lee Martin is now with Ramsgate.
Third round ties will take place over the weekend of Saturday and Sunday 6th and 7th January.
The Blues are entering the competition at the third round stage for the first time since 2018/19.
Last season, Town came through rounds one, two and three before losing to eventual Championship title winners Burnley in the fourth after a replay at Turf Moor.