"When you're pushing the frontier, it's not a sure thing", Musk said.
The first space tourist was Dennis Tito, an American businessman who in 2001 paid some $20 million to fly on a Russian spaceship to the International Space Station.
The ride will take place aboard a Big Falcon Rocket (BFR), which may not be ready for human flight for five years at least, Musk said.
At the time, Musk said the pair approached SpaceX about sending them on a weeklong flight and paid a "significant" deposit for the trip.
Nevertheless, Musk said the Japanese billionaire actually chose his company for the Lunar mission, and not the other way around.
But Musk cautioned that SpaceX may not meet its 2023 timeline for the lunar mission. There's always a chance that "something will go wrong".
"I know that sounds insane, and we don't usually meet our time lines, but I wanted you to know at least order of magnitude, that's what we're thinking", Shotwell said.
Asked why the company made further changes, Musk said he "did not like the aesthetics" of the previous version.
During the unveiling of the rocket, Musk said that the BFR already has its first passenger booked, but during the event, no names were offered.
This billionaire will be the first tourist to fly around the moon
SpaceX has been talking plans to send tourists around the Moon since early 2017.
Maezawa's journey to the Moon - scheduled to start in 2023 - is likely to last for about a week.
The BFR spacecraft's shape is reminiscent of the space shuttle, the bus-like USA spaceships that carried astronauts to space 135 times from 1981 to 2011.
Musk said the BFR is still in development and will make several unmanned test launches before it takes on passengers.
Two of Musk's fellow billionaires - Amazon's Jeff Bezos and Virgin Group's Richard Branson - also want to make a business out of space tourism. Blue Origin denied the report to CNN, saying ticket prices had not yet been set. This suggested that the company is still working on the design.
He recently criticized analysts during a Tesla earnings conference call, labeled a British diver in the recent Thai cave rescue drama as a pedophile, took a hit off an apparent marijuana-tobacco joint during a podcast interview, and tweeted that he had funding to take Tesla private but then announced the deal was off.
A Japanese fashion magnate and art curator, Yusaku Maezawa, is going to become the first private passenger on a trip around the moon - and it's going to be incredible, because he will not be going alone.
The ship will launch from Kennedy Space Center, in Florida, atop a huge white booster named the Big Falcon Rocket, or BFR.