The Ayrshire derby was one of 11 ties drawn at Murrayfield before the second leg of Celtic's Champions League third qualifying-round tie against Legia Warsaw, with five SPFL Premiership sides entering the tournament at this stage.
St Mirren were handed a home draw against Dunfermline, Partick Thistle visit Morton and newly promoted Hamilton Academical welcome Alloa Athletic.
The winner of the first-round tie between Queen's Park and Rangers will host Inverness Caledonian Thistle, with all matches to be played on August 26 and 27. Hibernian host Dumbarton, and Stenhousemuir welcome Hearts.
Holders Aberdeen do not enter until the third round, along with Celtic, Motherwell, Dundee United and St Johnstone.