Two dozen seats were ripped out and lighting, tables and chairs in the bar and fanzone were substantially vandalised.
The Football League One club stepped in to provide a stadium for Welsh side The New Saints, for their Europa Conference League campaign.
This is because their own stadium, Park Hall, meets Uefa regulations for staging qualifying games but not matches in the main draw of European competitions.
The stadium is a 31 minute drive away from Shrewsbury's stadium, Croud Meadow.
The Oswestry-based Saints hosted Djurgarden, a team in Sweden's top flight with a history of rowdy fans.
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Just last month the Stockholm derby against Hammarby was suspended as police withdrew permission for the match due to fireworks being thrown by Djurgarden fans.
Behaviour which spilled over in England despite the Swedish team defeating The New Saints 1-0.
Shrewsbury have released a statement following the match. It reads: "Shrewsbury Town are angry and saddened to report the Croud Meadow has been left vandalised by Djurgarden supporters.
"As a club, we took the decision to host TNS and their Europa Conference League matches in our home to boost tourism in the county and bring European football to Shropshire.
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"However, we have been left dismayed by supporters of Djurgarden after they caused widespread damage.
"More than two dozen seats have been ripped out of the West Stand. There has also been substantial damage to lighting, tables and chairs in Smithy's Bar and in the FanZone.
"Alongside destroying property, Djurgarden fans also took it on themselves to cover all three areas in graffiti.
"Just a few pictures of the damage are included in this story above.
"We have spoken to Djurgarden as we continue to assess the damage and are working with them to repair the damage - however this work may not be done in time for our next fixture against Blackpool on Wednesday
"As a club we would like to stress this vandalism is nothing to do with TNS - with the damage clearly caused by Djurgarden supporters."