Governing body UEFA said the match was "delayed due to crowd disturbance" and that it would start at 1940 local time (1740 GMT) after TV footage showed supporters of the German team making their way towards the home fans and throwing flares.
Police intervened but the players had not started warming up shortly before the scheduled 1845 local time kickoff.
Cologne said a UEFA meeting was "ongoing".
"Unfortunately the start of the game is delayed due to violent clashes between... both fan groups in the stadium and the stands. We are looking into the background," the German club said.
Cologne captain Jonas Hector (32) addressed the crowd through the PA system.
"We really want to play the game with you. We also want that game to take place. But we have to say that we do not like to see this," he said.
"We worked damn hard last year and in the playoff. And we would very much like to do this with you and we ask you to keep calm and support us as much as possible."
