Kadlec was leaving a Cologne night club with his girlfriend following their 1-0 win at Hoffenheim when he was approached by two people who identified themselves as supporters of regional rivals Cologne. They verbally abused him before hitting him in the face.
The Czech international will undergo surgery on Monday but said he hoped to be back in action against Hanover 96 next week.
"Even with a facemask I want to be there against Hanover," he said in a statement.
Cologne police confirmed the attack saying two unnamed men had broken the player's nose.
Leverkusen are sixth in the Bundesliga after their win at Hoffenheim on Saturday while Cologne, whose fans have repeatedly been in the spotlight for violent behaviour this season, are in the relegation playoff spot after drawing 1-1 with Stuttgart.