Wazir Mohammad Jawadi, a district administrator, said another child from the same family was wounded in the blast, which took place late yesterday.
Afghanistan is inundated with mines and other explosives left over from decades of war.
Elsewhere in Afghanistan, an official said Afghan security forces repelled an insurgent attack in the eastern Kunar province, killing 26 militants.
Gen. Abdul Habib Sayedkhaili, the provincial police chief, said that a police officer was killed in the fighting, which erupted when hundreds of insurgents tried to overrun Ghazi Abad district headquarters near the border with Pakistan. He said forces had prior intelligence about the attack and were prepared to repel it.
"If we had not had the support of the local people it would have been very difficult to repel the enemy's attack," he said.