The former world heavyweight champion threatened to ‘cave in’ Bellew’s skull, and made several other unsavoury comments, prior to his stoppage defeat at the O2 Arena.
Haye has now been summoned to appear before the BBBofC on 12 April, despite apologising for his remarks and making a donation to the organisation.
Robert Smith, the board’s general secretary, told BBC Sport: “Mr Haye was told to behave himself but the board have called him.
“He will now be given the opportunity to come and explain his behaviour,” he added.
At their first pre-fight press conference in November, Haye and Bellew came to premature blows while ‘facing off’, with Haye appearing to strike the Liverpudlian.
Bellew, meanwhile, was handed a suspended four-month ban in December after he called Haye out following his successful WBC cruiserweight title defence against BJ Flores.
The BBBofC described the pre-fight conduct of both boxers as “extremely disappointing” and reminded the pair to be “sensible” in the days leading up to their meeting.
After Bellew’s victory was confirmed, both he and Haye embraced in the ring and spoke of the respect they share for one another.
“He's the man, he beat me fair and square,” Haye said of Bellew. “If I want my stripes back I have to go past this guy, I have to go past him if I want to fight for world honours. I'm at his mercy, there's no rematch clause, but if the fans want it we can make it happen.”