Still, when asked by reporters if Musk would be a passenger, he left the door open to the possibility.
Musk said he would not reveal the price Maezawa paid for the Moon trip, but said it would be "free for the artists".
"I did not want to have such a fantastic experience by myself", said Mr Maezawa, wearing a blue sports jacket over a white T-shirt with printed with a work by the late painter Jean-Michel Basquiat.
Between six and eight artists will join the expedition called Dear Moon, which is now planned for 2023.
Maezawa plans on inviting artists from different disciplines including literature, film, visual arts, architecture and fashion.
But it is reliant on a rocket that has not been built yet, and Mr Musk cautioned: "It's not 100% certain we can bring this to flight".
On Monday, Mr Musk unveiled new artist impressions of the BFR and the spaceship which will carry passengers around the Moon. Those missions will depend on SpaceX's proven Falcon rockets.
For all the rocket trips into space in recent decades, no human has traveled into lunar orbit (let alone onto the surface of the moon) since NASA's Apollo missions ended in 1972.
If all goes according to plan, Maezawa and his artist crew could become the first-ever private lunar tourists in history. And now, it appears there will be only one person aboard. In 2012, he started the Tokyo-based Contemporary Art Foundation to support young artists. The amount that Maezawa paid for the trip was not disclosed.
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The week-long Moon mission is scheduled for 2023, with tests kicking off within the "two to three years", the newspaper reports.
The art project called #dearMoon was presented in a video released shortly after he and Mr Musk announced the moon flight. Musk did not name the clients a year ago or say how much they would pay.
A render of the Big Falcon Rocket or BFR. You have to be pretty loaded to score a tourist spot on a spaceship.
Musk's ultimate goal is to colonize Mars. "And what will they create?"
Musk's successes have recently been overshadowed by his behaviour and the struggles of his Tesla electric auto company to deliver.
He has alleged that a cave diver in Thailand who helped rescue stranded boys was a "pedo", smoked what appeared to be marijuana on a comedian's podcast, spooked Tesla investors with comments about the future of the electric vehicle maker, and admitted to exhaustion and use of the sleeping pill Ambien.
Before Monday's announcement, Musk last publicly described the BFR and showed renderings of the system at the 2017 International Aeronautical Congress. Last month he told the New York Times he was overwhelmed by job stress.
Earlier on Monday it emerged Mr Musk was being sued for defamation over his repeated claims that a British cave diver was a child abuser.
Elon Musk and SpaceX have been doing some very cool things over the past decade with rockets.