Around 30 fans were involved in the brawl, which broke out shortly after midnight in the centre of Cologne.
When police tried to intervene to separate the fans, they too were attacked. Other fans also joined the melee and threw bottles and a chair at the police officers.
One of the officers sustained head and hand injuries, while three others sustained less serious injuries. Around 75 people, largely fans of the Cologne club were temporarily detained while police took their details.
Five people were arrested but were released later on Friday. Police are now investigating serious assault, attempted freeing of a detainee and breach of the peace.
The situation was largely peaceful directly after the match when police escorted the 2,500 Belgrade fans away from the stadium and putting them in special trains to the Neumarkt district of town.