That match is being played at Hampden Park in Glasgow, with kick-off at 3pm.
Mo go into that tie on the back of a goalless draw at home to Alloa Athletic on Saturday.
That result leaves the Gable Endies as they were, sitting fourth in the table, but now on 28 points from 17 games, one place and one point better off than Alloa.
Their next league game is away to second-placed FC Edinburgh on Saturday, December 17, also kicking off at 3pm.
Manager Stewart Petrie is viewing Mo’s draw against Alloa as a point gained rather than two dropped coming after their 5-2 Scottish Cup third-round defeat at home to West of Scotland Football League premier division side Darvel the weekend before, telling the club’s Facebook page: “The biggest thing was trying to get a reaction to last Saturday.
“It wasn’t good enough. We were disappointed to let everybody down – fans, club, the whole lot – so we knew that, and we certainly got a reaction.
“I thought in the first half we were good – really good, in fact – considering Alloa are a good side and they’re obviously doing really well and have got some right good players.
“First and foremost, we were looking to keep a clean sheet. That was the big thing – let’s get back to being what the Montrose of old would be – and I thought we did that, so I was delighted with that side of things.
“Over the piece, I was really happy with the reaction to last Saturday.
“I still think there’s room for improvement and all the boys would agree. We can all do better and we’ll be striving to do that.”
Looking ahead to Mo’s cup tie against the Spiders, currently third in Scottish football’s second tier on 30 points from 17 games, Petrie, 52, added: “It’s a great occasion for us all – from staff to directors to players and coaches. It’s great. We’re going to enjoy it.
“They’re going brilliant under under Owen Coyle so it’ll be a tough game for us but it’s one we’ll thoroughly enjoy.
“There aren’t many times you get to go and coach players at Hampden so I’ll look forward to that.”