Celtic could face another meeting with cup bogey side Inverness in the fifth round of the William Hill Scottish Cup.
Inverness, who have twice knocked Celtic out of the tournament this century, will host Neil Lennon's side if they beat Dunfermline in an East End Park replay.
Rangers, who defeated Arbroath 4-0 on Sunday, will face 2010 winners Dundee United at Ibrox.
Scottish Cup fifth round draw:
Hibernian v Dundee/Kilmarnock
Motherwell v Morton
St Mirren/Hamilton v Ross County
Inverness CT/Dunfermline v Celtic
Ayr v Falkirk
Rangers v Dundee Utd
Hearts v St Johnstone
Aberdeen v Queen of South
Ties to be played over the weekend of 4 February 2012.