Maezawa, who recently split up from actress girlfriend Ayame Goriki, 27, has said he plans to take artists on the flight to inspire works based on the experience, in a project he dubbed Dear Moon.
The documentary, titled Full Moon Lovers, will stream on AbemaTV, which is backed by online ad agency CyberAgent and broadcaster TV Asahi and targets a younger audience that is turning away from traditional TV.
Applicants must "be interested in going into space and able to participate in the preparation for it" and "be someone who wishes for world peace", the website states.
Applications close on January 17 and Maezawa will select his partner by the end of March.
The documentary is the latest high-profile move by the billionaire, who is also giving away $9 million to his Twitter followers to try and spark debate in Japan about the merits of the idea of basic income.