The 61-year-old victim, Masaaki Takahashi, was found fatally stabbed in his cab Wednesday night in Yokosuka, south of Tokyo, about a half-mile from the U.S. naval base.
The case follows a furor over a series of criminal allegations against U.S. servicemen in Japan, where some 50,000 American troops are based. The outrage prompted U.S. military officials to impose restrictions on servicemen.
A sailor in his 20s - sought by U.S. officials after he was reported missing several weeks ago - was apprehended early Saturday, Kyodo News agency said. The man's credit card was found in the slain driver's car, local media reports said.
No charges have been filed.
Cmdr. David Waterman, spokesman for Commander U.S. Naval Forces Japan, confirmed that navy officials caught "a deserter," but would not say if he was a suspect in the killing. He refused to provide any other details.
Kanagawa prefectural police, where Yokosuka is located, also would not comment on whether they had identified a suspect.
Japanese anger over the U.S. military presence has grown in recent months following an alleged rape in February of a 14-year-old girl by an American serviceman on the southern island of Okinawa, as well as an alleged gang rape of a Japanese woman by U.S. Marine Corps officers in Iwakuni, southern Japan last year. Other alcohol-related incidents have inflamed sentiment.
Both cases were dropped by the Japanese authorities, but the U.S. military is continuing its own investigations of the cases.
Inside Takahashi's cab, investigators discovered about 60,000 yen (about US$600) in cash in a bag and tens of thousands of yen in his pockets, according to local media, which also suspected a payment dispute between the driver and his last passenger may have led to the killing.