Dunfermline have a glamour tie at Ibrox to play the holders Rangers, while Ross County and Dundee United will re-enact last season's Scottish Cup final.
Aberdeen host Raith, Hearts visit Falkirk, Queen of the South play St Johnstone and Brechin face Motherwell.
Fourth round draw in full:
Rangers v Dunfermline Kilmarnock v Hibernian Aberdeen v Raith Rovers Falkirk v Heart of Midlothian Celtic v Inverness Caledonian Thistle Ross County v Dundee Utd St Johnstone v Queen of the South Brechin City v Motherwell
All ties will be played on 21 or 22 September.
Source: BBC Sport
Source: BBC Sport