At a SpaceX event on Monday in Los Angeles, Musk did not clarify how much Maezawa would pay for the journey, according to TechCrunch.
On Monday, Mr Musk unveiled new artist impressions of the BFR and the spaceship which will carry passengers around the Moon.
First announced on 27 February 2017, the Falcon Heavy/Crew Dragon customer mission would have seen two private citizens - one of them Maezawa and the other a chosen passenger of his - launched into a lunar free-return trajectory for a flyby of the moon and return to Earth. He is best known elsewhere for paying a record $110 million past year for a 1982 painting by the late Jean-Michel Basquiat.
Maezawa added that he won't be travelling alone as he'll be bring artists along with him.
'These artists will be asked to create something after they return to Earth, and these masterpieces will inspire the dreamer within all of us'.
The announcement of this trip, is one of many steps SpaceX has taken to realize the company and the Big Falcon Rocket's mission: "To help advance rocket technology to a point where we could potentially become a multi-planet species and a true spacefaring civilization", Elon Musk said during a press briefing tonight. Musk has said he hopes to construct the first prototype by mid-2019 and then launch several tests from the company's rocket facility in South Texas. "This is my lifelong dream", Maezawa said.
To make the trip happen, SpaceX is designing a huge, three-finned Big Falcon Rocket, sometimes known as the "Big F****** Rocket". The moon trip would last four to five days, he said.
He wondered on stage what John Lennon, Coco Chanel, Michael Jackson or Andy Warhol would have created had they seen the Moon up close.
SpaceX has announced the identity of its first passenger to fly on its forthcoming BFR spacecraft, headed around the moon in 2023.
Maezawa has chartered a flight aboard the company's Big Falcon Rocket, which is still being developed, for a slingshot trip around the Moon as soon as 2023. He wouldn't disclose the price Maezawa is paying for the ride, but did say that the billionaire is funding "a material percentage" of the BFR system's estimated $5 billion development cost.
Mr Maezawa did not immediately say who will be on his guest list for the spaceflight, but in response to a question from a reporter he said he would consider inviting Mr Musk.
Falcon Heavy's maiden flight was shown as part of SpaceX's evolution towards BFR.
SpaceX chief Elon Musk pauses while speaking during the 67th International Astronautical Congress (IAC) in Guadalajara, Mexico. Whoever the mystery passenger is will be among the first space tourists to fly with a commercial company.
The BFR's principal goal is to carry settlers and their stuff to Mars, 100 passengers at a time.
"As far as me going, I'm not sure", Musk responded.