"Find out who's flying and why on Monday, September 17," SpaceX said in a tweet on Thursday.
The person's identity will be revealed on Sept. 17, Space Exploration Technologies Corp. said in a tweet. Asked whether he'd be the first passenger, Musk posted an emoji of a Japanese flag.
Musk's SpaceX and Richard Branson's Virgin Galactic LLC are among companies that are attempting to commercialize space travel. In July, billionaire Branson said he hoped to be sitting on a spaceship going to space before the end of the year.
SpaceX this month successfully launched a commercial satellite from Florida, marking the company's 16th mission of 2018.
The company also has a contract to ferry American astronauts to the International Space Station.