Holders Rangers will host Raith Rovers in the Scottish Cup quarter-finals as Darvel and Falkirk learned Ayr United are their potential opponents.
Hearts will host Celtic in an all-Premiership meeting, while Kilmarnock go to Inverness.
Rangers disposed of Partick Thistle in an epic 3-2 win on Sunday, while Celtic defeated St Mirren.
Raith stunned top flight Motherwell 3-0, while giant-killing Darvel and Falkirk play on Monday night.
The Ayrshire side play in Scottish football’s sixth tier but stunned Premiership Aberdeen in the fourth round. Their meeting with Falkirk at Recreation Park is live on BBC Scotland.
Ayr United required extra time on Saturday to eventually canter to victory over Elgin City.
Full draw
Inverness Caledonian Thistle v Kilmarnock
Heart of Midlothian v Celtic
Rangers v Raith Rovers
Darvel or Falkirk v Ayr United
Ties to be played on weekend of Saturday 11 March