The defense ministry said that the incident followed "an engagement with an insurgent" and that no civilians were involved.
It added that the seven were arrested Thursday by Royal Military Police, but did not name the marines. While the ministry said the marines were not arrested in Afghanistan, it would not specify where the arrests took place or give any further details on the alleged murder.
"The investigation will now be taken forward and dealt with by the Service Justice system," the Ministry of Defense said in a statement, adding that "as with any serious incident of this nature, there will be an internal review to identify lessons learned."
It is believed to be the first time U.K. servicemen have been arrested on suspicion of murder over events or incidents that took place in Afghanistan.
Last year, a British soldier was jailed for stabbing a 10-year-old Afghan boy with a bayonet. The boy survived the incident, which happened in March 2010.
Britain has 9,500 troops in Afghanistan—the second largest foreign force after the United States—based in the southern Helmand province.
About 500 troops will leave this year, ahead of the withdrawal of all international forces at the end of 2014.