Naval Criminal Investigative Services confirmed the arrests of two Marines and one sailor — all based out of Camp Pendelton in California — in an emailed statement to Newsweek.
Oslo announced this week that it would ask the U.S. to substantially increase the number of Marines it stations in Norway.
The training is held every year as part of the Foul Eagle joint military drills.
Nearly 7,000 U.S. troops are taking part in the 37th Cobra Gold drills held in Thailand.
General Robert Neller told troops in Europe that times have changed and "maybe we need to change something."
More than 400 marines have been doing training activities together, including shirtless wrestling in the snow.
A window fell from a CH-53 helicopter in the second such incident in less than a week.
The U.S. Marines have ramped up their presence in Europe in the past few years.
The U.S. Marine Corps said the incident was under investigation but gave no additional information.
The Marine Corps has been rattled by a scandal involving a private Facebook group and its surreptitious distribution of explicit images of women in the armed forces.
President Donald Trump also has reportedly weighed sending up to 1,000 U.S. troops to Kuwait.
The U.S. Marines were taking part in a training exercise at the camp in North Carolina.