No one has flown to the moon since the final mission of NASA's Apollo program.
SpaceX gave no further details, but said more information would follow on Monday.
The webcast is embedded below.
Now, the Hawthorne, Calif. -based company says it's ready to unveil the name of the first person to take the trip and the reason for the journey.
The BFR (also known as the Big Falcon Rocket) is SpaceX's upcoming two-stage reusable spaceship system that will weigh 9.7 million pounds and be capable of taking a 330,000-pound payload to Mars and lower-Earth orbit (LEO). Asked whether he'd be the first passenger, Musk-who's also the chief executive officer of Tesla Inc. -posted an emoji of a Japanese flag.
In February, SpaceX debuted the long-awaited Falcon Heavy, which became the world's most powerful operational launch vehicle, the report said.
However the passengers were never named and the flight has yet to materialise.
American astronauts Neil Armstrong and Buzz Aldrin became the first men to explore the lunar surface in 1969, a moment seen and heard around the world when Armstrong declared "one small step for man, one giant leap for mankind". "And we believe we can do this with the revenue we receive from launching satellites and servicing the space station". "That would be on a Dragon 2 spacecraft and a Falcon Heavy rocket, which is due to do its maiden launch this summer".
"We've been approached to do a crewed mission beyond the moon from some private individuals", he said at the time.