The soldier was one of two wounded during a firefight between British troops and "suspected terrorists", said a military spokesman.
Two suspects were held during the operation, which took place in the Garmat Ali tribal area, north of Basra.
Some 8,000 British troops are stationed in southern Iraq. The death brings the total of British dead there to 114.
The BBC's correspondent in Baghdad Jonny Dymond said the troops had been sent out to apprehend suspects intelligence sources had identified were involved in the insurgency.
They met resistance, which is when the two soldiers sustained gunshot wounds. They were evacuated to a military hospital where one later died of his injuries, the Ministry of Defence said.
The name of the dead soldier has been withheld until next of kin are notified.
The MoD said in a statement: "An operation was conducted by multi-national Forces in Iraq in the early hours of this morning to apprehend those associated with terrorist activities
"We can confirm that as a result of this operation, two men suspected of involvement in serious crime and terrorism in the Basra province have been apprehended."
British forces spokesman Major Charlie Burbridge said it has been an intelligence-led operation, and that the mission's objective had been achieved.
"We have been pleased with the outcome of the operation - it went according to plan. But we do mourn the loss of one of our soldiers."
He said further details about the significance of the operation would later be released.
Transfer of duties
Lieutenant Tom Mildinhall, 26, and Lance Corporal Paul Farrelly, 27, both of the 1st Queen's Dragoon Guards (The Welsh Cavalry), were killed when a Land Rover they were travelling in was hit by a roadside bomb in north west Basra on 28 May.
Last month it was announced that security in one of Iraq's 18 provinces was being handed to local forces for the first time since the country was invaded in 2003.
Defence Secretary Des Browne said the decision to give Iraqi troops control of power in Muthanna was a "milestone" for the Iraqi people.
BBCGüncelleme Tarihi: 20 Eylül 2018, 18:16