Yoshie Sato, 56, was found beaten and unconscious in Yokosuka on Tuesday, and later died of internal bleeding. Police believe the victim was attacked during a robbery on her way to work, according to news reports.
The case risked further inflaming local opposition to plans to build an American military airstrip in the southern island of Okinawa and base a U.S. nuclear-powered warship at Yokosuka for the first time.
The 21-year-old sailor, who was not identified, was being held at the base in Yokosuka pending the investigation into the killing, U.S. Naval Forces Japan said in a brief statement, which called the sailor "a potential suspect."
The sailor was based on the aircraft carrier Kitty Hawk and has been in Japan since May 2004. He has been in the Navy for about two years and Japan was his first assignment, the Navy said.
Japanese news reports said the sailor had already confessed to killing Sato, but that report could not be confirmed by police.
Tatsuya Ishihara, spokesman for Kanagawa Prefectural Police, said a request by Japanese interrogators to question the sailor had been approved by U.S. authorities.
Another police spokesman, who spoke on condition he only be identified by his last name, Kobayashi, said that police had questioned the sailor at the Navy base Friday, but he refused to provide any further details.