Dundee United’s meeting on Tayside with Spartans was postponed due to a waterlogged pitch, with the tie taking place on Tuesday 17 February (19:45 GMT).
Motherwell’s trip to take on Aberdeen, who beat Celtic in last year’s final, is the following day (19:45).
Celtic needed extra-time to eventually get by Dundee on Saturday, while Partick Thistle beat Elgin City and Dunfermline overcame Kelty.
Earlier on Sunday, Rangers hammered Queen’s Park 8-0 to continue Danny Rohl’s impressive domestic run of results.