It will be the club's first match against SPL opposition since they were demoted to the Scottish Third Division.
Celtic have been handed a home tie against Raith Rovers, while Hearts will host Livingston.
Celtic vs. Raith Rovers
Rangers vs. Motherwell
St Mirren vs. Hamilton Academical
Queen of the South vs. Dundee United
Hearts vs. Livingston
Dunfermline Athletic vs. Aberdeen
St Johnstone vs. Queen's Park
Stenhousemuir vs. Inverness Caledonian Thistle
The ties will be played in the week commencing September 24.