Joshua was midway through his first face-off with Alexander Povetkin, the challenger to his IBF, WBA and WBO heavyweight titles, when Miller barged onto the stage.
Joshua’s attention immediately switched to Miller and some frank words were exchanged as they were kept apart.
The world heavyweight champion was in New York for the launch of DAZN, the streaming site which will provide Sky Sports with 16 new US fight nights.
He met Povetkin in person for the first time since their fight on September 22, live on Sky Sports Box Office from Wembley Stadium, was announced.
But Miller, a local New Yorker who will be one of DAZN’s first recruits, crashed their stare-down.
Wearing sunglasses and shouting at the champion, unbeaten Miller swiftly provoked an angry response from Joshua.