The Red Bull driver sat down to speak to reporters at the team's hospitality suite in Suzuka, but then said, "I'm not speaking before he's leaving", and gestured at a journalist from The Guardian newspaper.
The journalist asked Verstappen if his demand was because of a question he had asked the driver last season, to which Verstappen replied "yes" and told him to "get out".
The reporter left and Verstappen continued with the press conference.
The reporter later told AFP that the incident stemmed from a question he had asked Verstappen after the Dutchman missed out on a fifth world title to Lando Norris by two championship points at the Abu Dhabi Grand Prix in December.
The question centred on the impact of a penalty that Verstappen had picked up for ramming Mercedes driver George Russell at the Spanish Grand Prix in June.