The news came on Friday amid accusations that British troops in Iraq have abused prisoners and shot dead innocent civilians.
“The Attorney General has referred the case of a British soldier formerly serving in Iraq to the Crown Prosecution Service for its views on whether criminal charges should be brought,” the statement said.
“The case concerns an alleged unlawful killing in the course of an arrest.
“The case currently under consideration by the CPS was referred to the Attorney General after charges were dismissed by the soldier’s Commanding Officer. In these circumstances, the case cannot be tried by court martial,” it added.
It said it had asked the police for assistance in the investigations, which followed an inquiry by the Military Police, but gave no further details.
Britain has promised to fully investigate allegations of abuse and illegal behaviour.
The United States Army on Thursday discharged one of its own soldiers and sentenced him to one year in jail after he admitted abusing prisoners in Iraq’s notorious Abu Ghraib jail.
He is expected to give evidence against a number of other US soldiers accused of abuse.
The scandal has sent shockwaves through the Arab world and piled more pressure on the United States and its main ally Britain.
British anti-war campaigners, led by the Stop the War Coalition, plan to stage a demonstration through central London on Saturday calling for the immediate withdrawal of all British troops from Iraq.