A US Marine has been arrested on suspicion of murder after a woman's body was found in a hotel in Okinawa, Japan, local officials say.

Japanese Prime Minister Sanae Takaichi described the crime as a "brutal and heinous" robbery and murder. She said she had urged the US to "enforce stricter discipline" of its personnel.

Japan's public broadcaster NHK identified the victim as Yagi Anna, 39, and the suspect as Devin Jacob Ballard, 20, who is stationed at US Marine Corps Air Station Futenma.

"We are actively cooperating with Japanese authorities in response to allegations of serious criminal actions by a Marine," the Marine Corps said on social media, extending condolences to the victim's family.

Japanese Defence Minister Shinjiro Koizumi said the woman's body was discovered early Saturday morning in a hotel in Naha City, the capital of the Okinawa prefecture.

"Such an incident is utterly inexcusable and fills me with strong indignation," Koizumi wrote on social media, adding that "incidents and accidents involving U.S. military personnel cause significant anxiety to the local community and must never occur".

The US Embassy in Tokyo said that it was fully cooperating with the Japanese government and local police. Japan's foreign ministry said it summoned US ambassador George Glass to discuss the incident on Sunday.

Okinawa is home to several US military bases and tens of thousands of American troops.

Okinawa Governor Genta Koja says the prefecture has repeatedly demanded that the US take action to prevent such incidents, and said he sees the alleged crime as a sign of a lack of discipline.

"The fact that this kind of event has happened again leaves us no choice but to conclude that the US military's efforts in maintaining discipline, educating personnel, and other such measures are completely ineffective," he said.