Meanwhile, the visitors are without a win in their four previous league outings and were eliminated from the FA Cup at this stage last year by Buxton.
Match preview
Shrewsbury are without a win in their previous three league outings, so perhaps Salop will welcome the break from League One action here.
However, it will not be a cause for concern for Steve Cotterill as his side are sitting reasonably comfortably in 11th place in the table.
Last time out against Portsmouth, Elliot Bennett fired Shrewsbury in front with their only shot on target in the game before Zak Swanson's first senior goal for Pompey salvaged a point for the home side at Fratton Park.
Town enjoyed an exciting FA Cup run last season that saw them beat non-league Stratford 5-1 in the first round. The Shrews then secured victory at Carlisle before taking on Liverpool in a dream tie at Anfield in the third round, losing 4-1.
They will be eager to venture into another magical run starting on Saturday at Montgomery Waters Meadow, where a place in the second round is up for grabs.
Meanwhile, York beat Bury AFC in the fourth qualifying round on October 15 to make it to this stage, and they will be aiming to cause an upset when they travel to Shropshire on Saturday.
However, their performance this weekend will need to be an improvement on what John Askey has seen from his side in recent weeks, as the Minstermen are without a win in the last four league matches.
They were beaten comfortably by Southend United last time out courtesy of goals from Gus Scott-Morriss and Shaun Hobson.
However, despite the poor run of form, York are only four points adrift of the playoff places in the National League and most of their success this season has been built on their defensive record, conceding 17 goals in their 17 league outings - only three sides have conceded fewer.
Shrewsbury Town form (all competitions):
W
W
L
L
L
D
York City FA Cup form:
York City form (all competitions):
L
W
D
L
D
L
Team News
Matt Pennington returned in midweek after a period on the shelf due to injury, so he could start once again here.
However, Cotterill may opt to rotate his side with a game against Oxford United coming up next Wednesday.
Aiden O'Brien and Julien Dacosta both picked up injuries in training last week, and are expected to be absent for this FA Cup clash.
The away side will be without striker Lenell John-Lewis after he was forced off early due to a calf injury against Southend.
However, in similar fashion to the hosts, Askey may rotate his starting XI as the Minstermen will travel to Boreham Wood next Tuesday in the National League.
Shrewsbury Town possible starting lineup:
Marosi; Pennington, Dunkley, Flanagan; Bennett, Leahy, Bayliss, Winchester, Shipley; Saydee, Bowman
York City possible starting lineup:
Ross; Sanders, Kouogun, Kerr, Crookes; Kouhyar, Fallowfield, Pybus, Mafuta; Duku, James
We say: Shrewsbury Town 2-0 York City
This game brings two teams in similar form against each other, and as the cliche goes, anything can happen in the cup.