Makoto Shimomi, 51, who reportedly runs a Liechtenstein-based investment fund, and Mie Shimomi, 48, disappeared after leaving their luxury condo in Tokyo's upmarket Ginza district on December 7th.
The couple, who had a number of homes both in Japan and abroad and reportedly frequented Monaco's social scene, told friends they were going to a party 150 kilometres (90 miles) outside the capital.
Police say there was no such event and they now believe the pair were kidnapped and strangled.
Television footage taken from a helicopter showed a large blue tent over a patch of soil in Saitama, just outside Tokyo, where police reportedly found the two bodies buried in shallow graves.
Local media reported investigators have confirmed the man's body to be that of Shimomi and are close to confirming the identity of the other as his wife.
Kyodo News reported on Tuesday that police arrested a man on an Okinawa island in connection with the deaths.
Police on Tuesday told AFP they were looking for a number of men in the case.
Reports say all of those being sought are acquaintances of the dead man.
Jiji Press and Nippon Television said one man had been arrested on a sub-tropical island in Japan's far south.
Violent crime is rare in Japan and the country's media seizes on unnatural deaths to feed a public fascination.