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The hosts had the better of the chances against their League One rivals and were denied three times by the woodwork in the second half.
Chances were in short supply during the first half. Shrewsbury's best opportunity in the early stages fell to Ivan Toney but the Newcastle loanee's header from a Louis Dodds cross was comfortably saved by Alex Cairns.
Dodds then had a close-range effort blocked as Shrewsbury, who reached the fifth round last season before bowing out to Manchester United, pushed for a breakthrough.
Fleetwood midfielder Bobby Grant's overhead kick cleared the bar before visiting captain Nathan Pond's header from Kyle Dempsey's free-kick was acrobatically saved by Jayson Leutwiler, diving low to his right.
Shrewsbury hit the same post twice within a minute early in the second half. A low shot from Dodds beat keeper Cairns but came out off the inside of a post before Junior Brown's flick from a Dom Smith cross also struck the woodwork.
The Shrews continued to look the most likely side to break the deadlock and Toney's 25-yard free-kick clipped the top of the bar before Grant hammered a late shot from distance narrowly wide for Fleetwood as deadlock ensued.
Report supplied by the Press Association.
Match ends, Shrewsbury Town 0, Fleetwood Town 0.
Second Half ends, Shrewsbury Town 0, Fleetwood Town 0.
Attempt missed. Amari'i Bell (Fleetwood Town) header from the centre of the box is too high.
Foul by Junior Brown (Shrewsbury Town).
Kyle Dempsey (Fleetwood Town) wins a free kick in the defensive half.
Ethan Jones (Shrewsbury Town) is shown the yellow card for a bad foul.
Foul by Ethan Jones (Shrewsbury Town).
Conor McLaughlin (Fleetwood Town) wins a free kick in the attacking half.
Substitution, Shrewsbury Town. Ethan Jones replaces Ivan Toney because of an injury.
Delay in match Ivan Toney (Shrewsbury Town) because of an injury.
Foul by Ivan Toney (Shrewsbury Town).
Conor McLaughlin (Fleetwood Town) wins a free kick in the attacking half.
Attempt missed. Bobby Grant (Fleetwood Town) left footed shot from outside the box misses to the left following a set piece situation.
Foul by Gary Deegan (Shrewsbury Town).
Amari'i Bell (Fleetwood Town) wins a free kick on the left wing.
George Waring (Shrewsbury Town) wins a free kick on the right wing.
Foul by Bobby Grant (Fleetwood Town).
Ivan Toney (Shrewsbury Town) hits the bar with a right footed shot from outside the box from a direct free kick.
Ivan Toney (Shrewsbury Town) wins a free kick in the defensive half.
Foul by Conor McLaughlin (Fleetwood Town).
Ryan McGivern (Shrewsbury Town) wins a free kick on the right wing.
Foul by David Ball (Fleetwood Town).
Substitution, Shrewsbury Town. George Waring replaces Ian Black.
Attempt blocked. Louis Dodds (Shrewsbury Town) right footed shot from outside the box is blocked.
Corner,  Shrewsbury Town. Conceded by Ashley Hunter.
Attempt missed. Louis Dodds (Shrewsbury Town) header from the centre of the box misses to the left.
Attempt blocked. Ashley Hunter (Fleetwood Town) right footed shot from outside the box is blocked.
Adam El-Abd (Shrewsbury Town) wins a free kick in the defensive half.
Foul by Ashley Hunter (Fleetwood Town).
Junior Brown (Shrewsbury Town) wins a free kick in the defensive half.
Foul by Bobby Grant (Fleetwood Town).
Foul by Ian Black (Shrewsbury Town).
Chris Long (Fleetwood Town) wins a free kick in the defensive half.
Substitution, Fleetwood Town. Chris Long replaces Devante Cole.
Delay over. They are ready to continue.
Delay in match Conor McLaughlin (Fleetwood Town) because of an injury.
Ryan McGivern (Shrewsbury Town) is shown the yellow card for a bad foul.
Foul by Ryan McGivern (Shrewsbury Town).
(Fleetwood Town) wins a free kick in the defensive half.
Bobby Grant (Fleetwood Town) is shown the yellow card for a bad foul.
Shrewsbury and Fleetwood face a replay at Highbury after playing out a goalless draw in the second round of the FA Cup.