The 27-year-old Briton apologised after making derogatory remarks about women and being critical of homosexuality and abortion.
"Tyson Fury has made comments in the media that have caused offence to members of our society," the BBBC said.
"However, there is no suggestion that he has broken the law by exercising his right to freedom of expression. In such circumstances, the Stewards of the British Boxing Board of Control have been advised that it cannot interfere with his basic human rights."
The Board made it clear to Fury that as arguably the holder of the most prestigious title in sport, there were "heavy responsibilities" on him to avoid making "controversial, non-boxing comments".
Fury, who won the world heavyweight title by outpointing Ukrainian Wladimir Klitschko in November, told the Board that he never intended to cause offence and regretted doing so.
"He has assured the Stewards that he understands the responsibilities upon him," the BBBC said.
(Reporting by Ed Osmond; editing by Toby Davis)
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