The tie was one of four all-Scottish Premiership encounters picked out the hat as Sir Alex Ferguson helped conduct the draw.
In the others, Dundee United will host Kilmarnock, Hibernian travel to Dingwall to face Ross County and Ferguson's former club, Aberdeen, will play Partick Thistle at Firhill.
Two of the clubs the former Manchester United manager played for, Falkirk and Rangers, were first out of the hat and will play at the Falkirk Stadium.
Elsewhere, Inverness host Morton, St Johnstone are at home to Livingston and St Mirren get the chance to avenge their League Cup defeat by Queen of the South when they return to Dumfries.
Motherwell make the short journey to Coatbridge to face Lanarkshire neighbours Albion Rovers while there are other local derbies between Brechin and Forfar and Alloa and Stirling.
Falkirk v Rangers, Albion Rovers v Motherwell, Culter/Berwick v Dumbarton, Clyde v Stranraer/Auchinleck Talbot, Dundee United v Kilmarnock, Queen of the South v St Mirren, Stenhousemuir/Annan v Fraserburgh, Brechin v Forfar, Alloa v Stirling, Ross County v Hibernian, Dundee v Raith Rovers, St Johnstone v Livingston, Partick Thistle v Aberdeen, Hearts v Celtic, Ayr v Dunfermline, Inverness v Morton