Rangers will play Celtic in their Scottish Cup semi-final at Hampden Park on Sunday 17 April.
The Scottish Football Association said the Old Firm derby will have a 12:00 GMT kick-off at the national stadium.
Dundee United will take on either Hibernian or holders Inverness Caledonian Thistle in the other semi-final on Saturday 16 April at 12:15.
BBC Scotland will broadcast live television coverage of the second tie, also being played at Hampden.
Caley Thistle will host Hibs in their replay on 16 March following a 1-1 draw at Easter Road.
Meanwhile, Hibs or United could face three of their biggest-ever fixtures within a week, should either reach the Scottish Cup final and be involved in the Premiership play-offs.
United are currently bottom of the top flight, while Hibs are third in the Championship, with the second bottom Premiership side destined to play the final against the winner of a series of play-offs from the division below
The dates for the final will be changed should they feature a team in the cup final.
If that applies to either Hibs or Dundee United, the first leg of the play-off would be played on Tuesday 17 May, with the second leg on the 25th, four days after the Scottish Cup final.
There is a scenario where Rangers could be involved in this too, although it seems unlikely they will surrender a 12-point lead at the top of the Championship and be forced into a play-off.