Richard Roretana Tutaki, 33, was arrested on Tuesday and was refused bail. He will remain in custody until he appears in court again next Tuesday, the Weekend Herald reported.
An arrest warrant was issued after he failed to turn up to face criminal charges in Auckland District Court.
New Zealand Professional Boxing Association president Lance Revill said Williams would still be fighting but a new opponent was being sought, Fairfax New Zealand reported.
It's understood that Tutaki had trained either very little or not at all for the fight, and there were concerns in boxing circles about his physical and mental condition, the report cliamed.
Williams, 26, has been linked with a return to the NRL with the Sydney Roosters next year, although both parties insist no formal agreement has been struck.
He joined the Chiefs squad for training this week in Hamilton and replied simply "maybe" when asked whether he might extend his stay in Hamilton if all went well.
Williams controversially walked out on the Canterbury Bulldogs mid-season in 2008, switching to rugby and joining French club Toulon.
He returned to New Zealand in 2010 to play for Canterbury and the Cruaders and was part of the All Blacks' World Cup-winning squad last year.