The pick of the round is a last-four tie between Hearts and Rangers at Tynecastle, where Steven Gerrard’s side were defeated 2-1 only two weeks ago.
Hibernian, who avoided a giantkilling act with a 4-1 victory over Lowland League BSC Glasgow, have been rewarded with a home match against Inverness Caledonian Thistle.
The winners of the replay involving St Mirren and Motherwell will entertain the winners of the Aberdeen-Kilmarnock tie.
The full draw:
Hibernian v Inverness Caledonian Thistle
St Mirren or Motherwell v Aberdeen or Kilmarnock
St Johnstone v Celtic
Hearts v Rangers.
Matches to be played on the weekend of 29 February/1 March