The two Demnark giants are situated approximately 10 kilometres apart and have shared a rich history of hatred towards one another.
But their latest run in, which has been labelled 'revolting', certainly took things to a new level.
With Brondby trailing 1-0 in the 85th minute, the home fans threw dead rats at Copenhagen's Ludwig Augustinsson, while he was lining up a corner kick.
Play was stopped while the dead rats were moved off the pitch, with the Copenhagen players and the stewards assisting in the removal.
Brondby later released a statement about the incident, with the club's sport director Troels Bech condemning it.
"When we stand here after the game, we are obviously annoyed that we had to leave the field without points, but it is equally unfortunate that there are some visitors for today's match who could not figure out how to behave properly," Bech said in the statement.
"We will now look all the video material and pictures ... [and] engage in dialogue with groups of supporters in the hope that together we can identify the right person and make sure that he gets quarantined from the stadium.
"We have Denmark's most atmospheric football stadium and the home ground of Denmark by far the best fans, and a single individual should not ruin it for the greater community."
The incident failed to have any effect on the outcome though, with Copenhagen hanging on for a 1-0 win to extend their lead over Brondby by 12 points at the top of the Superliga table.