Sky Sports will cover the match at Tynecastle with a 12.30pm kick-off time.
That will be followed by Celtic’s trip to either Lothian Thistle Hutchison Vale or East Kilbride, which has also been switched to Sunday and will kick-off at 3pm and be broadcast live by the BBC.
Celtic’s will learn their opponents on Wednesday when the two sides meet in a rearranged fixture after the initial tie was postponed.
Rangers’ tie against Kilmarnock will also be shown live, on 6 February. This match will precede the rest of the fifth round matches with a 12.30pm kick-off, also in front of the Sky cameras.
This will mean the postponement of Celtic’s league game with Dundee the following Tuesday.
Meanwhile, the SPFL has announced the date of Hearts’ rearranged fixture with Inverness CT. The game was postponed in December and will now take place on March 1.