Police spotted a crowd of people known to be hardcore hooligans in a central square and surrounded them, according to spokesman Gerog Blaszyk. When the officers moved in, he said, the fans began throwing bottles and shooting fireworks as they fought police in riot gear.
Details were still emerging from a chaotic situation. At least one fan was seen receiving treatment for facial cuts.
In a separate incident, German hooligans also attacked police near the jumbo screen that shows soccer games in the 32-team tournament. No other details were immediately available.
For much of the day, German police had been working with their Polish counterparts to identify and arrest Polish hooligans from the throngs massing for the match between the neighboring countries. At least 60 Poles were arrested and did not offer resistance, police said.
That operation started early and included four men found to have knives near the stadium, police said.
"Our Polish spotters identified them as their troublemakers from back home," Dortmund police spokeswoman Saskia Schneider said.
Under German law, people can be held up to 48 hours if police think they may commit a crime.