Holders Celtic will host Kilmarnock in the fourth round of the Scottish Cup, while Rangers welcome Highland League side Fraserburgh to Ibrox.
There will be a Dundee derby at Dens Park and Aberdeen make the short trip to Elgin City.
Hibs will be at home against Clydebank as Hearts visit Brechin City, while St Johnstone take on Motherwell.
Championship leaders Falkirk won 3-1 at East Kilbride on Monday evening and will meet divisional rivals Raith Rovers next.
Fourth-round matches will be played on the weekend of 18-19 January.
Scottish Cup fourth round draw
Dumbarton v Airdrieonians
Cove Rangers v Forfar Athletic
Dundee v Dundee United
Dunfermline Athletic v Stenhousemuir
Falkirk v Raith Rovers
St Johnstone v Motherwell
Queen's Park v Montrose
Ross County v Livingston
Hibernian v Clydebank
Rangers v Fraserburgh
Brechin City v Hearts
Queen of the South v St Mirren
Hamilton Academical v Musselburgh Athletic
Elgin City v Aberdeen
Broxburn Athletic v Ayr United
Celtic v Kilmarnock