Scottish Cup holders Hearts will visit Dunfermline, conquerors of Rangers, in the fourth round of the tournament.
Morton's reward for beating Kilmarnock is a trip to Motherwell and Celtic face a journey to Division One Livingston.
Highland League outfit Deveronvale are at home to Partick Thistle, Inverness take on either Dundee Utd or St Mirren and Falkirk host St Johnstone or Ayr.
Last year's beaten finalists Gretna will travel to meet the winners of Wednesday's Aberdeen v Hibs tie.
Dundee or Queen of the South will be at home to either Cowdenbeath or Brechin City.
Tennent's Scottish Cup fourth-round draw:
Motherwell v Morton
Dunfermline v Hearts
Inverness Caledonian Thistle v Dundee United or St Mirren
Falkirk v St Johnstone or Ayr United
Deveronvale v Partick Thistle
Dundee or Queen of the South v Cowdenbeath or Brechin City
Aberdeen or Hibernian v Gretna
Livingston v Celtic
Ties to be played on February 3 and 4
606 DEBATE: Your reaction to the draw