The other semi-final pits Kilmarnock against Ayr United in an Ayrshire derby.
First Division outfit Falkirk have already knocked out Celtic's Old Firm rivals Rangers and Dundee United out of this season's competition.
Ayr will be aiming to upset Kilmarnock after already seeing off Inverness, Hearts and St Mirren in previous rounds.
The ties will be played on January 28 and 29.
Steven Pressley joked that his young Falkirk side should be handed the trophy if they get past Celtic.
"It is a huge incentive and if we achieve that then they should just give us the trophy, to be perfectly honest," he said with a smile.
"It would be an incredible achievement for this young team, if we were to come through Rangers, Dundee United and Celtic.
"The vast majority of our team have never experienced playing at Hampden or in a national semi-final while Celtic have been there, seen it and done it.
"But all the pressure lies with Celtic and we can go there and enjoy the occasion.
"We will prepare properly and with a real belief that we can win the game.
"It will take us to play at optimum levels to achieve that but we have proved we are capable of that already in this competition."
The semi-finals will not take place until the end of January, which prevents Falkirk possibly taking advantage of the pressure Celtic are under at the moment, as they struggle to keep pace with Rangers.
However, that does not bother the former Scotland defender, who as a player had spells at Rangers, Dundee United and Celtic.
"I am quite happy that there are several months before the game because there will be a real anticipation around the club," said Pressley.
"The players will be vying for places and so it will create a real sense of competition and that is a good thing for us.
"Don't think I am not aware of how big a challenge it is for this club and what type of performance it will take but we will certainly be going in to the game believing that we can get a result.
"Anything is possible with the right attitude."
Kilmarnock defender Manuel Pascali declared himself "absolutely buzzing" after the draw handed Ayrshire the biggest derby in its history.
The 30-year-old, speaking moments after the draw, said: "I'm buzzing because I know what this means for all the supporters from Kilmarnock and Ayr.
"I was lucky to play two times against them three years ago and the atmosphere was unbelievable. It's going to be a great, great match.
"All the Killie and Ayr fans have been waiting for this draw. I'm absolutely buzzing, seriously, because every footballer wants to play this kind of match.
"I'm not young anymore. I wish I could have another 10 years in front of me, but this could be one of the biggest games I've played, it will be full of emotion."
The whole-hearted Pascali relished the intensity of his first Ayrshire derby experiences and feels he knows exactly what the rivalry means to supporters.
"I had only been in Scotland for five months and everyone was talking about this match," he said.
"But I didn't realise it was so big until someone told me 'you can be relegated, it doesn't matter, but you have to win this match'.
"That told me how important it was and this one will be the biggest derby in the history because if you win you are going to go to the final.
"So if you're an Ayr United fan and Kilmarnock reach the final you have to watch the TV or go to the cinema. It will be the same for us. It will be a great day of football."
Full semi-final draw:
Falkirk v Celtic
Ayr v Kilmarnock




 





