The incident occurred during a news conference after Ukrainian Vitali Klitschko retained his WBC heavyweight belt, scoring a unanimous points decision over challenger Chisora in Munich's Olympic Hall.
British media reports said Chisora, who threatened to "shoot and burn" Haye, was arrested at Munich airport early Sunday while Haye was still being sought after he not available at his hotel for questioning.
Haye, who was beaten in July by Vitali's younger brother Vladimir in Hamburg, retired in October but was offered a way back with a fight against the senior Klitschko this year.
Haye, who had been working as a television pundit for the Chisora-Vitali fight, became agitated by comments made by Klitschko's manager, Bernd Boente, that he would no longer get a fight with the older sibling.
"Contrary to David Haye, Dereck Chisora really went for it and really tried," Boente said in the post-fight news conference.
"You don't want to fight David Haye, no?" Haye, who was at the back of the conference room, replied.
Boente then said: "You had an offer, you didn't accept it, now you are out. You are out. Out, out, out. You cannot talk yourself back into the fight, you have no belts. Chisora showed heart, contrary to you. You showed your toe."
After the altercation with Boente, Haye got into an argument with his fellow Briton Chisora which resulted in the duo trading punches.
Haye's manager Booth suffered a cut above his eye following the scuffle.
The incident was the latest controversy to surround Saturday's fight in Germany. Chisora, who had slapped his rival at the weigh-in Friday, spat water into Vladimir's face during the pre-fight ceremonies.
"I'm totally disappointed, it went a little too far, the sport of boxing shouldn't be like that," Klitschko told the BBC after watching the fight between the two British boxers.
"Bloody faces in the press conference... I'm really surprised."
British Boxing Board of Control General Secretary Robert Smith plans an investigation and hinted that Haye would now find it difficult to have his licence renewed if he decided to come out of retirement.
"I am extremely disappointed and disgusted really," he said.
"It does not do the sport any good or Britain any good. Unfortunately it was like Brits abroad and I am very disappointed.
"We would have to go through the normal process and deal with any outstanding matters which have to be considered. First of all we would have to listen to what David Haye has to say but he has not done himself any good and neither has Mr Chisora."
(Writing by Sudipto Ganguly in Mumbai and Mark Meadows in London; editing by Patrick Johnston and John Mehaffey)