Czech international Kadlec was attacked early on Sunday outside a nightclub where he had been with team-mates following their 1-0 win over Hoffenheim and needed surgery on Monday to fix his broken nose, Bayer Leverkusen said.
Leverkusen said the attackers were listed in a hooligan directory as Cologne supporters, prompting an apology from their regional rivals.
"I was informed of Sunday's incident and immediately contacted [Bayer boss] Wolfgang Holzhaeuser to apologise to Michal Kadlec in the name of Cologne," Cologne Chief Executive Claus Horstmann said in a statement.
"We are also offering our help in the criminal prosecution of this case and will check what legal options we have ourselves.
"It is not possible that players from other clubs cannot freely move around Cologne."
Kadlec said he wanted to return to action this week against Hannover 96 as his club battle for a European spot, even with the help of a face mask.
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