Lizarazu slapped with fine
It happened in a heated training session when Kovac went in with a robust challenge on the World cup winning full-back, which prompted Lizarazu to strike the Czech star in the face.
Fellow Bayern players stepped in to separate the feuding pair and Lizarazu was kneed in the face as he was being pulled away from the skirmish.
Tensions are running high at the club following their poor run in the Bundesliga and their exit from the first phase of the Champions League, in which they failed to win a single game.
The Munich ace was hauled into boss Otmmar Hitzfield's office and immediately fined é¼10,000 for his involvement in the fracas. The manager confirmed "Lizarazu started the fight, so he will be fined."
Lizarazu, who was once fined for slapping German legend Lothar Matthaeus, told L'Equipe: "At Bayern, you have to earn respect because it's like a wolf pack."
He said he had warned Kovac about his actions, prior to the challenge: "I told him several times to be careful but sometimes, words are not enough.
"I can appreciate this incident has come at a bad time for Bayern but I don't regret anything.
"I don't stab people in the back, I don't spend my time speaking about other people behind their back, when I have a problem, I settle it in an upfront way."
The Euro 2000 winner went on: "It is unfair that I'm the only one to be fined over the incident because there are always two people in a fight and this is not just a result of one training ground incident."