Celtic travel to Ross County, while Rangers host Queen of the South in the last 16 of the Premier Sports Cup.
Dundee United will travel to Livingston and Hearts take on Kilmarnock in all-Scottish Premiership ties, while Championship favourites Dundee are at home to Falkirk.
The draw was made following Aberdeen’s 3-0 victory against Raith Rovers on Sunday. They are away at Annan Athletic in the next round.
Elsewhere, Motherwell host Inverness Caledonian Thistle and Partick Thistle are at home to Arbroath.
The full last-16 draw
Rangers v Queen of the South
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Partick Thistle v Arbroath
Motherwell v Inverness Caledonian Thistle
Livingston v Dundee United
Dundee v Falkirk
Annan Athletic v Aberdeen
Hearts v Kilmarnock
Ross County v Celtic
The first round of games take place on the weekend of August 30-31.