Footage emerged over the weekend of the Australian stand-off launching drunken, foul-mouth abuse at a female McDonald’s worker.
Kelly, shortlisted for Man of Steel last season, has been spoken to by club management and the East Yorkshire club says the matter has been addressed "internally".
However, there has been no detail given about what, if any, action has been taken against the 27-year-old former Hull KR player.
Kelly has scored three tries and set up another eight in nine appearances for Lee Radford's side so far this term.
Hull, who beat champions Leeds Rhinos on Thursday to move up to fourth, face Catalans Dragons in Perpignan this Saturday.