With their struggling team second from bottom in Denmark's Superligaen, Brondby fans stormed the pitch following a 1-0 victory after extra time against their bitter city rivals.
"The sad epilogue to the game is that we see thousands of Brondby fans running onto the pitch," police inspector Michael Kristiansen, adding the fans were arrested for disorder and breaches of firework regulations.
"The object was clearly to get into a confrontation with FC Copenhagen fans," Kristiansen said.
Brondby's head of security Emil Bakkendorf condemned the fans involved.
"It is shameful and unacceptable. This is a grotesque development. I strongly condemn this," he told Danish radio station DR.