The Czech Republic international was out with friends in Koln after his side's 1-0 win over Hoffenheim at the weekend, before an altercation between himself and fans of the Billy Goats ended with the former Sparta Prague man going to hospital.
"I was stunned," Kadlec told Express. "My nose was immediately bleeding heavily, and my friend was shocked.
"The men had shown themselves to be Koln fans and started insulting me. Then, I felt a violent blow.
"It was something I have never seen, either in Koln or my native Czech Republic."
Kadlec will have surgery on Monday, but hopes to play in Leverkusen's next game against Hannover using a protective mask over his face.