The launch of the first-ever privately funded tourist flight beyond the International Space Station is tentatively targeted for late 2018, Musk told reporters on a conference call.
SpaceX said Monday two private citizens have paid money to be sent around the Moon late next year, in what would mark the furthest humans have ever traveled to deep space.
The United States has not sent astronauts to the Moon since NASA's Apollo missions of the 1960s and '70s.
"We are excited to announce that SpaceX has been approached to fly two private citizens on a trip around the moon late next year," said a statement by CEO Elon Musk.
"This presents an opportunity for humans to return to deep space for the first time in 45 years and they will travel faster and further into the solar system than any before them."
The tourists, who were not named, "have already paid a significant deposit," Musk's statement added.
They will ride aboard the California-based company's Crew Dragon capsule, which is scheduled for its first unmanned test flight later this year.
It is based on the design currently used to send cargo to the International Space Station, with upgrades to allow for human transport.