British Prime Minister Tony Blair, at a meeting in South Africa, responds to questions about the video taped beatings.
The military said it arrested the man on Sunday night, but has declined to identify him, refusing even to confirm whether he was a serving soldier or where the arrest was made.
Earlier on Sunday, British Prime Minister Tony Blair promised a full investigation into the video, stills from which were run in the Sunday edition of the British newspaper News of the World.
The newspaper did not reveal the source of the video, which was allegedly shot in southern Iraq in 2004.
Blair, attending a meeting in South Africa, said Britain takes the allegations of mistreatment seriously. They "will be investigated very fully indeed."
Blair also defended British soldiers.
"The overwhelming majority of British troops, in Iraq as elsewhere, behave properly, are doing a great job for our country and for the wider world."
Brig. Martin Rutledge, a British military spokesman, said the Royal Military Police had started an "urgent" investigation.
The video shows a group of soldiers chasing down stone-throwing youths, catching four and dragging them inside a walled compound where the soldiers beat the youths with batons and kicked them. The cameraman can be heard laughing as he watches the beatings and says, "Naughty little boys."
The paper said it was confident the video was genuine.