The Warriors were defeated in Dumfries last season in the group stage and have also been drawn with East Kilbride FC – another team who got the better of them on their last cup meeting.
Completing the Warriors’ group is boss Brown Ferguson’s former club Hamilton Academical and Albion Rovers.
Queen of the South
The competition begins on July 15, with four further matchdays on July 18, July 22, July 25 and July 29.
Drawn matches in the group stages will go straight to penalty kicks after 90 minutes where the sides will play for a bonus point.