David Haye & Dereck Chisora could face prison over brawl
Haye is suspected of grievous bodily harm - a crime which, if proven, carries a prison sentence of six months to 10 years, prosecutors said.
Chisora, who admitted his behaviour was "inexcusable", is under suspicion of malicious injury, which carries a jail sentence of up to five years, and making a "threat".
The latter is a lesser offence punishable by a fine or imprisonment of up to one year.
Haye and Chisora clashed after Chisora's defeat by defending WBC heavyweight champion Vitali Klitschko on Saturday night.
The Zimbabwean-born boxer issued a statement where he apologised "wholeheartedly" for his "part in the regrettable scenes both before and after what was to be the biggest night of my career."
He added: "Whilst my behaviour was inexcusable, there were many things that went on behind the scenes that ultimately caused my frustrations to boil over, however this is of course no excuse.
"Despite all of this, the bottom line is, I have let my family, my team and worst of all the sport I love down."
Haye said in a statement he would, if requested, "happily assist the boxing authorities with any investigation they wish to launch".
He added: "I realise I am no angel - and don't mind a bit of professional trash-talk to help raise boxing's profile - but, during my 21 years in the sport, I have never been involved in, or even witnessed, such a serious fracas."
Haye left the country on a plane before he could be questioned by police.
"I decided to leave the venue and return to my hotel, a move which I hoped would defuse the situation," his statement added. "However, Chisora's team were staying at the same hotel as me and, in light of the threats Chisora made in front of the world's media, it seemed more appropriate for me and Adam to leave the hotel as quickly as possible.
"Consequently, I left Munich on an earlier flight on Sunday morning and have been thinking about what happened ever since, as well as replaying the incident many times via YouTube. It goes without saying, I am bitterly disappointed to have been a part of what transpired on Saturday evening."
Chisora and his trainer Don Charles were arrested at the city's airport before being released on Sunday evening. Chisora did not speak to journalists when he arrived back at London's Heathrow airport on Sunday night.
On top of a police investigation, the British Boxing Board of Control General Secretary, Robert Smith, says Haye and Chisora could face life bans from the sport.
"It's a possibility," Smith told BBC Radio 5 live. "The board have many powers. They can fine, they can suspend and they can withdraw a licence."
The British Boxing Board of Control (BBBofC) have confirmed that Chisora has been called to appear before a BBofC hearing on Wednesday, 14 March in relation to his conduct before and after his fight against Vitali Klitschko in Munich.
"With regard to Mr David Haye, Mr Haye is not a licensed boxer with the British Boxing Board of Control and therefore no longer under our jurisdiction."
Although Haye has retired from the sport, the board could choose to effectively ban him by denying him a licence if he seeks to fight again.
The scenes unfolded after Haye showed up at the news conference to confront Vitali Klitschko, who he believes changed his mind on a potential fight between the pair.
But that sparked a verbal exchange with Haye and Chisora squaring up to each other before a brawl ensued.
Chisora accused Haye of "glassing him", before saying at least four times that he would shoot the former WBA heavyweight champion.
He added: "If David don't fight me, I am going to physically burn him."
Smith said the scuffle ranked among of the lowest moments in British boxing history.
"I'm very disappointed and very saddened that, in a sport I love, I have to deal with this," he added.
"I have to speak to the German Boxing Federation and German police and then take appropriate action. This is not good, it's bad, we have to deal with it accordingly."
Chisora has had part of his fight purse withheld by the World Boxing Council after slapping Klitschko at the pre-fight weigh-in on Friday.
Chisora spat water towards Klitschko's brother, Wladimir, moments before Saturday night's bout began.
More controversy followed when Chisora exchanged words with the Klitschko brothers after the result was announced.