The Sun newspaper reported that a sergeant and a private from the Mercian Battle Group have been arrested over claims that they abused an Afghan boy and a girl, both aged about 10, and filmed the incidents.
"We are aware that an allegation has been made concerning alleged inappropriate behaviour by two servicemen in Afghanistan," a Ministry of Defence spokesman said in a statement.
"The Royal Military Police (Special Investigations Branch) has launched an investigation into this. We take any such allegation extremely seriously.
"It would be inappropriate to comment further while an investigation is ongoing."
The allegation comes less than a week after a video emerged showing US Marines urinating on the corpses of militants in Afghanistan.
Britain has some 9,500 troops in Afghanistan, mainly based in Helmand where they are battling a Taliban insurgency. Britain intends to pull out all its combat troops by 2015.