The man, who is in his 60s and from the Durham area, was detained at the Montgomery Waters Meadow during Tuesday night's League One match which ended in a 1-1 draw.
The suspect remained in police custody on Wednesday morning, West Mercia Police said.
Chief Superintendent Paul Moxley said: “There is no place for racism in football, or in any place in society and we take a zero tolerance approach to it.
“We will be working with Shrewsbury Town Football Club and our own hate crime officers to identify any victims.
"Anyone who wishes to contact us in relation to this incident can do so via our online reporting form.”