One England fan and seven Serbs are facing criminal charges and tournament bans after a huge fight broke out between 150 people before the game.
German police say the clashes started when England fans tried to enter a steakhouse that was full of Serbia supporters.
An England fan was taken to hospital but discharged himself to go and watch the game.
Reports say tables and chairs were thrown and that some involved in the fighting sustained head injuries.
Peter Both, the police chief in Gelsenkirchen, said in a statement: “The Serbian fan group was already in the restaurant and obviously ate there, and then a larger group of English fans then tried to get into this restaurant as well. And that’s exactly what sparked the dispute.
“What we can hardly say now, of course, in retrospect, is did the Serbs refuse entry to the English or did the English provoke the Serbs? Of course, this can hardly be brightened up afterwards.
“The fact is that when they tried to enter the pub, there was an immediate physical altercation.
“We subsequently made several detentions. We carried out a total of around 50 identity checks. We took eight fans into custody before the game, who were then unable to watch the game.”
Mr Both then explained why more arrests were not made when so many people were involved in the fighting.
He said: “If we had predicted in the opening press conference that there would be one detention [of an England fan], then we would all have gladly taken it.
“Why did the police only take seven or eight people into custody when there were 150 people running around? The first issue is that you can only take someone into custody if you can make an individual accusation.
“So the ones where we can say either via video recordings or via personal evidence from deployed police officers, I can prove that you threw this chair, you threw this glass, you hit that one, have seen that, I can prove it – only those are then taken into custody accordingly.
“We have everyone’s personal details and are now in contact with the organiser, with UEFA, because we would already make a recommendation to UEFA. They can see if these people still have tickets for other games and we would recommend that these tickets are then blocked for the next games.”
England will return to Gelsenkirchen for their round of 16 tie if they win their group.
The Three Lions head to Frankfurt next to play Denmark before finishing off the group stages against Slovenia in Cologne.