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.