Holders Rangers will take on Motherwell as they look to maintain their grip on the trophy.
Well overcame Dundee United in the quarter-finals, while Rangers proved too strong for Kilmarnock.
Celtic tackle Aberdeen in the other semi-final.
Aberdeen saw off First Division Falkirk in the last eight, while Celtic overcame St Johnstone.
Co-operative Insurance Cup semi-final draw:
Aberdeen v Celtic
Rangers v Motherwell
Ties to be played January 29-30.