The Blues visit the League Two outfit on Weds, Aug 1 (7.45pm ko), in a game agreed as part of the deal that saw us sign young keeper Joe Hart for £600,000 last summer.
The Shrews have recently moved to the 10,000-seater stadium from their old Gay Meadow ground, which had been their home for 97 years.
It will be another journey into the unknown for City as they will also play at Doncaster's Keepmoat Stadium for the first time on July 14 in their opening friendly.