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.
Under a U.S.-Japan agreement, the Navy would have to hand over the sailor if Japanese authorities requested it.
The U.S. Navy said it was cooperating closely with Japanese police, and had imposed a temporary curfew requiring Navy personnel to be back on base by midnight until next Monday.
"The entire Navy community in Japan is deeply saddened by this incident and will immediately implement a period of reflection to collectively demonstrate sympathy for the tragic loss of life," the Navy release said.
Reflecting the sensitivity of the case, the U.S. Embassy issued a statement Friday expressing regret for the crime.
"The U.S. military and the American people are deeply shocked and saddened by this event," U.S. Ambassador Thomas Schieffer said in a written statement.
Japanese Defense Agency chief Fukushiro Nukaga told reporters both Japan and the United States had to work harder to stop such crimes.
"Japan-U.S. alliance can be built only through cooperation from the community, and we must make utmost efforts to prevent recurrence of such misconduct," he said.
In 1995, an uproar over the rape of a 12-year-old girl by three U.S. servicemen on Japan's southern island of Okinawa triggered massive protests and led to the relocation of an air base to a less densely populated part of the prefecture.
The rape case also resulted in an agreement with the U.S. military that it would hand over American suspects in serious crimes to Japanese authorities for pre-indictment investigation.
About 50,000 U.S. troops are stationed in Japan under a joint security pact, but Tokyo and Washington agreed in October to move 7,000 Marines from Okinawa to the U.S. territory of Guam, and shift within Japan some of the remaining troops.
Senior foreign affairs and defense officials from the two countries will hold talks in Washington next week on the realignment of U.S. forces, the Japanese Foreign Ministry announced on Friday.