Referee Kenny Bayliss stopped the fight in the sixth round to the annoyance of Gotti, who then lashed out at 46-year-old Mayweather.
The ring was then swarmed with team members from both sides as Bayliss struggled to contain the drama.
Gotti III, 30, is the grandson of former New York crime boss John Gotti.
The melee kicked off a number of fights amongst the crowd in the FLA Live Arena in Florida and backstage.
