Officials said it was not known what type of leaflet was involved.
"Sadly one of the boxes failed to fully open and on landing caused serious injuries to an Afghan child," a Royal Air Force spokesman said in a statement.
"The child was treated at the local medical facility in Kandahar where despite the best efforts of staff she died as a result of her injuries."
The MoD said it was believed to be the first time a civilian had been killed by such an airdrop.
Britain has about 9,000 troops in Afghanistan, mainly in Helmand. Some 40 British soldiers have been killed in Afghanistan in the past two months and 218 have died there since the US-led invasion in 2001, a greater death toll than during the Iraq war.