Rangers will host Dundee United in the Scottish Cup following the draw for the fifth round at Hampden.
Holders Celtic face a trip to the winners of the Inverness CT v Dunfermline fourth-round replay, while Queen of the South will take on Aberdeen.
Hearts will host St Johnstone and Morton travel to Motherwell.
The draw was conducted by Chelsea boss Andre Villas-Boas and Italian World Cup-winner Marcello Lippi.
Hibernian manager Pat Fenlon, whose team beat Cowdenbeath 3-2 on Saturday, said: "I didn't really mind who we were drawn against as long as we were at home.
"It's going to be difficult again, no matter which team comes through.
"We're happy enough to be at home. It could have been easier, it could have been harder, so we'll take what has come our way."
Aberdeen have a chance to restore some pride from their 2008 semi-final defeat by Queen of the South when they host the Dumfries side, but Dons boss Craig Brown is keen to avoid the build-up being overshadowed by that 4-3 Hampden defeat.
"We have a home draw and if we fail to progress it will be our own responsibility and totally our own fault," said Brown
"We will have to be focused on the game and treat them with great respect as we do for every opposing team and make sure there is no cup shock.
"I would encourage the media not to focus on the previous game between the sides in this competition. It is completely different."
First Division leaders Ross County will visit the winners of the replay between St Mirren and Hamilton, while Motherwell welcome Morton to Fir Park.
Motherwell beat Morton 3-2 at Cappielow in pre-season and manager Stuart McCallv was happy with the draw.
"I'm pleased, you just want to be at home," said McCall.
"I actually spoke to Andre Villas-Boas before the draw and asked him to make sure we were at home so well done to him for that.
"We played Morton in pre-season and it was a cracking game.
"We're well aware of the good threats they have but we've avoided the SPL and we're at home so we're pleased.
"But when the tie comes around we'll have to be at our best."
Scottish Cup fifth-round draw
Hibernian v Dundee/Kilmarnock
Motherwell v Morton
St Mirren/Hamilton v Ross County
Inverness/Dunfermline v Celtic
Ayr v Falkirk
Rangers v Dundee Utd
Hearts v St Johnstone
Aberdeen v Queen of the South
Ties to be played on 4-5 February