Fury directed a series of expletive-ridden tweets at both the retired Lennox Lewis and future opponent David Haye after Lewis had told reporters he would "probably knock him [Fury] out - inside a round".
Fury was fined £3000 in March for making homophobic tweets and the BBBC will take a dim view of Wednesday night's messages, some which appeared to follow a similar vein, with others making numerous violent suggestions.
The Board's general secretary, Robert Smith, has been sent a transcript of the offensive tweets and will discuss the matter with the organisation's stewards before deciding on a course of action.
It is likely Fury will be called before the Board to explain his comments and he is set to receive a stiffer fine and a warning as to his future conduct, but a decision to strip his licence is unlikely.
Fury's scheduled showdown with Haye was postponed last month when Haye sustained a cut in training just a week before the fight. The bout has since been rearranged for February.
Lewis, meanwhile, has dismissed reports he is preparing to make a comeback to fight one of the Klitschko brothers. Lewis tweeted that he has no intention of stepping back in the ring at the age of 48. "A hypothetical answer to a hypothetical question does NOT equal reality #NoComeback", before adding: "I'm not stepping back in the ring but I AM looking for the next crop of new talent!"
The response will kill off rumours Lewis was preparing to accept a world record purse in excess of $100m to provide the Klitschkos with some much-needed competition. Wladimir Klitschko defended his world title in Moscow last Saturday night with a routine victory over the widely regarded best available challenger, Alexander Povetkin.
Lewis last fought when he beat Vitali Klitschko in June 2003, and despite sporadic reports to the contrary, he has resisted the temptation to make a comeback.