Musk said that he will be flying on the company's future massive rocket, dubbed the "Big Falcon Rocket" (BFR), which is scheduled to be launched somewhere around 2023.
"I wish to create incredible works of art for humankind", Maezawa said.
Maezawa is chief executive of Japan's largest online fashion mall, and is the 18th richest person in Japan with a fortune of $3 billion, according to the business magazine Forbes.
Musk would not say what the trip would cost, but did say that the design of the almost 400-foot tall rocket had evolved recently, with the first flights to orbit coming in two to three years.
"I want to share this experience and things with as many people as possible", Maezawa said. He said he often mused about what artists like Basquiat or Andy Warhol might have come up with if they'd traveled into space.
Maezawa referred to Earth's longtime love affair with the moon, Beethoven's "Moonlight Sonata", and Van Gogh "Starry Night", and other works of art that have been inspired by the moon, "our planet's constant partner".
Maezawa didn't immediately say who will be on his guest list for the spaceflight, but in response to a question from a reporter he said he'd consider inviting Musk.
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"It's risky to be clear", Musk said.
According to Musk's presentation [PDF] past year, the mighty BFR will stand 118 metres tall when erected on its launchpad, and will be able to lift 150 tons into low Earth orbit with the help of a massive central booster, making it the most powerful rocket ever to fly.
SpaceX plans a lunar orbit mission. The Apollo 13 planned moon landing was diverted due to an explosion on the spacecraft, and the three crew members were forced to instead fly by their intended target and return home.
NASA is shooting for its own flyby of the moon, with a crew, around 2023. Two years later would mark the last time NASA astronauts would visit the lunar surface.
Musk himself has had a rocky year.
"This would be a long loop around the moon", stated Mr. Musk in regard to the private citizen flight of BFR. Musk did not name the clients past year or say how much they would pay.
The Big Falcon Rocket has not been built and not even Musk is willing to guarantee it will happen.
He wrote on his caption: 'My mission to go around the moon, as the first private passenger, will represent the imagination and curiosity of all people. (The British diver has sued him for defamation). And last month he tweeted that his new jet's interior is being fashioned by luxury label Hermes.