Premier will also screen Rangers' rivals Celtic's match with Clyde the following day. The game at Broadwood will have a 1.30pm kick-off.
The Saturday evening tie will either be Arbroath or Falkirk entertaining Hearts. The game, which starts at 7.20pm, will be shown by BBC Scotland.
The date of the other BBC Scotland match will depend on which team makes the fifth round. Hibs and Dundee United will battle it out on Tuesday for the right to face BSC Glasgow.
If Dundee United progress then the match will be shown on Friday night at 7.05pm.
If Hibs live up to their tag as pre-match favourites, then they'll travel to Glasgow on the Sunday for a 12noon kick-off.