A Scottish Championship side is guaranteed a place in the Scottish Cup final after Hibernian were drawn against Falkirk in the semi-finals.
The other tie will be decided after Celtic and Dundee United replay, and the conclusion of the postponed tie between Inverness Caledonian Thistle and Raith Rovers on Tuesday.
Saturday's match at Caledonian Stadium was called off following heavy rain.
Celtic will host United in their replay after Sunday's 1-1 draw at Tannadice.
The match is scheduled to take place on Wednesday 18 March.
Hibs had earlier thrashed League Two side Berwick Rangers 4-0 at Easter Road, while Falkirk edged out Championship rivals Queen of the South 1-0 on Friday.
The Bairns have won two of the three league meetings between the sides this season, both 1-0, while their latest ended in a 3-3 draw at Easter Road in January.
Both semi-finals will take place at Hampden Park on the weekend of 18 and 19 April.
Scottish Cup semi-final draw
Inverness Caledonian Thistle or Raith Rovers v Celtic or Dundee United
Hibernian v Falkirk
Ties to be played 18/19 April