Holders Celtic will travel to Easter Road to face Hibernian in the quarter-finals of the Scottish Cup.
Aberdeen will host Premiership rivals Kilmarnock or Rangers, while Partick Thistle will play Hearts at home.
And there will be a Championship clash between Dundee United and the winner of the Highland derby replay between Ross County and Inverness.
Brendan Rodgers' side defeated St Johnstone 5-0 to book their place in the last eight on Sunday.
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- Scottish Cup: Reaction to draw and Highland derby tussle
Scottish Cup quarter-final draw in full:
Aberdeen v Kilmarnock or Rangers
Dundee United v Ross County or Inverness Caledonian Thistle
Partick Thistle v Heart of Midlothian
Hibernian v Celtic
Ties to be played weekend of 2 March 2019.