The arrests by the Royal Military Police are apparently related to an incident in Afghanistan last year, when 3 Commando Brigade was based in Helmand, Afghanistan.
The MoD said that the incident followed an "engagement with an insurgent" and no civilians were involved.
"The investigation will now be taken forward and dealt with by the service justice system. These arrests demonstrate the Department and the Armed Forces'' determination to ensure UK personnel act in accordance with their rules of engagement and our standards," the BBC quoted a MoD spokesman, as saying.
"It would be inappropriate to make any further comment while the investigation is under way," he added.
According to the report, some 23 servicemen from the 3 Commando Brigade lost their lives in 2011 during a summer tour of duty that encompassed the height of the fighting season, while many more were injured.
The MoD is now likely to be liaising with 4 Mechanized Brigade, the UK force now in command of Task Force Helmand, to ensure that all necessary force protection measures are taken in case, the report said.