Scottish FA Youth Cup holders Hibernian were given a home draw against Queen's Park in the last eight of this season's competition.
Dundee will host Celtic while Kilmarnock will make the trip north to face Aberdeen.
The last tie to be drawn was Rangers v Cove Rangers.
All ties are scheduled to be played on Friday, 25 January 2019.
Scottish FA Youth Cup Fifth Round Draw 2018-19
Dundee v Celtic
Hibernian v Queen's Park
Aberdeen v Kilmarnock
Rangers v Cove Rangers