The West Mercia force is asking for help identifying several men it says were responsible for both disorder and racially aggravated public order offences.
The abuse happened after Shrewsbury played a pre-season friendly away at Hereford last week.
Police have released images of the suspects taken by officers' body-worn cameras.
Sergeant Mark Jones said: “We would very much like to identify and speak to the men in the images captured on body-warn cameras who we believe can help further our investigation.
“Please call me on 07971 634328 or visit our website and our 'tell us more' section quoting incident number 337i of 20 July 2021.”
Shrewsbury Town won the pre-season friendly game at Edgar Street 2-1.