Neil Lennon's side were paired with the Greenock outfit hours before they were due to discover their opponents in the Champions League group stages.
Premiership leaders Inverness also have a trip to Dundee while Queen of the South's reward for knocking out holders St Mirren is a trip to Tynecastle to face Hearts.
Scottish Championship leaders Hamilton host St Johnstone after knocking out Kilmarnock while Stranraer, the conquerors of Ross County, will face Hibernian at Easter Road.
Elsewhere, Livingston host Motherwell and Aberdeen travel to Falkirk.
League Cup third round draw: Hibernian v Stranraer, Dundee v Inverness, Celtic v Morton, Livingston v Motherwell, Hearts v Queen of the South, Falkirk v Aberdeen, Dundee Utd v Partick, Hamilton v St Johnstone.
Ties to be played on September 24 and 25.