Dozens of Polish fans reportedly attacked Croatian supporters and clashed with police following Sunday's match in the eastern town of Osijek, where Croatia defeated Poland 1-0.
Later, another altercation occurred between Polish and Croatian fans at a different location, though the details of this second incident were not provided.
“Dozens of people have been detained and the criminal investigation is ongoing,” the ministry said on social media.
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Authorities did not disclose the exact number of Polish nationals arrested.
However, at least five fans were detained in Osijek before the Group A1 match, during a fight in which a Polish national was injured.