Aberdeen manager Jimmy Calderwood was not too happy at drawing the trophy holders.
"To be honest it's a bit disappointing," he told his club's website.
"There had to be one all-SPL tie and surprise, surprise we are involved, with the only bonus being that we are at home.
"We never seem to get the roll of the dice in cup draws and this will be very, very tough."
Scottish Cup quarter-final draw in full
Queen of the South v Motherwell/Dundee.
Ross County/St Johnstone v St Mirren/Dundee Utd.
Hibernian/Rangers v Livingston/Partick Thistle.
Aberdeen v Celtic.
Ties to be played on 8/9 March.