The match at Tynecastle will be played on Sunday, January 20 and will kick off at 2.30pm. BBC Scotland will broadcast the match live.
Hearts’ tie is one of four to be picked for live coverage, with Premier Sports showing Cowdenbeath v Rangers on Friday, January 18 at 7.45pm.
There are two live matches on Saturday, January 19, with the Ayrshire derby between Auchinleck Talbot and Ayr United scheduled for 12.15pm (BBC Scotland) and Celtic v Airdrieonians for 5.15pm (Premier Sports).
Hibs will host League 2 side Elgin City on Saturday, January 19. The match will kick off at 3pm and will not be live on television.