West Mercia Police has echoed the football club's condemnation of the incident during Saturday's match against MK Dons at the Montgomery Waters Meadow stadium and asked for witnesses to get in touch.
Superintendent Stuart Bill said: " West Mercia Police is working with Shrewsbury Town FC to investigate reports of racist abuse at at Saturday’s match against MK Dons.
“We have spoken to a number of witnesses and our enquiries are continuing to ensure we have sufficient evidence to take robust action against those suspected of being responsible."
Supt Bill added: “There is no place for racism in football, or in any place in society, and we will always seek to secure a football banning order for those found guilty of racist abuse at a football match.
“We echo the words of the club in that we are bitterly disappointed and deeply appalled at the alleged racist behaviour.”
Any witnesses to the abuse are urged to get in contact via the police force's online reporting form at westmercia.police.uk/tua/tell-us-about/soh/seen-or-heard