The U.S. Navy is being rocked by a bribery scandal that federal investigators say has reached high into the officer corps and exposed a massive overbilling scheme run by an Asian defense contractor in exchange for ­prostitutes and other kickbacks.

Among those arrested on corruption charges are a senior agent for the Naval Criminal Investigative Service (NCIS) and a Navy commander who escaped Cambodia’s “killing fields” as a child only to make a triumphant return to the country decades later as the skipper of a U.S. destroyer. The i­nvestigation also has ensnared a Navy captain who was relieved of his ship’s command this month in Japan.

The chief executive and another company official of the Singapore-based defense contractor, Glenn Defense Marine Asia, were arrested last month at a San Diego harborside hotel after federal investigators lured them to the United States by arranging a sham meeting with Navy officials, according to court records and people involved in the case.

The unfolding investigation is shaping up as the biggest fraud case in years for the Navy. Federal prosecutors allege that Glenn Defense Marine, which has serviced and supplied Navy ships and submarines at ports around the Pacific Ocean for 25 years, routinely overbilled for everything from tugboats to fuel to sewage disposal.

Investigators are still assessing the scope of the alleged fraud, but federal court records filed in San Diego cite a handful of episodes that alone exceeded $10 million. Since 2011, Glenn Defense Marine has been awarded Navy contracts worth more than $200 million. The company also services ships from several navies in Asia.

The U.S. military has never been immune from contracting scandals, but it is extremely rare for senior uniformed commanders to face corruption charges.

“Allegations of bribery and kickbacks involving naval ­officers, contracting personnel and NCIS agents are unheard of,” said retired Adm. Gary Roughead, a former chief of naval operations who is a ­distinguished visiting fellow at the Hoover Institution at ­Stanford University.

According to court papers filed by federal prosecutors in San Diego, Leonard Glenn Francis, chief executive of Glenn Defense, and others in his company targeted Navy personnel serving in Asia and plied them with prostitutes, cash, luxury hotel rooms, plane tickets and, on one occasion last year, tickets to a Lady Gaga concert in ­Thailand.

In exchange, Francis sought inside information on ship deployments and pressed at least one high-ranking commander to steer aircraft carriers and other vessels to ports where his firm could easily overcharge the Navy for pierside services, the court documents allege.

Francis’ defense attorney, Edward Patrick Swan Jr., declined to comment on the ­allegations but said he expects the government will file ­additional charges.

Federal prosecutors in San Diego declined to answer specific questions. But Laura Duffy, the U.S. attorney for the Southern District of California, said the investigation was continuing. Court papers make references to several unnamed Navy officers who accepted favors from Francis, an indication that the investigation remains in its early stages.

Navy officials have ­identified Capt. Daniel Dusek, former commander of the Bonhomme Richard, as one of the targets of the investigation. He has not been charged but the Navy relieved him of command Oct. 2, citing the investigation.

The Naval Criminal Investigative Service has opened multiple investigations into Glenn Defense Marine since 2010. Until last month, none had resulted in charges. Last month, the Navy terminated three major contracts with Glenn Defense Marine worth nearly $200 ­million total.

At the company’s headquarters in Singapore, phone calls in recent days have gone unanswered. Reached via e-mail, Valeriane Toon, vice president for global communications, declined to comment.