Fazal Mohammad Ishaqzia, the governor of Panjwayi district in the southern Kandahar province, said the children killed Wednesday all belonged to the same family.
Kandahar Gov Samim Khopalwaq said they were all younger than 12.
Afghanistan has been at war for more than three decades and munitions left over from various conflicts regularly cause casualties.
In a separate incident, Interior Ministry spokesman Sediq Sediqqi says an army officer was arrested yesterday with 19 kilogrammes of heroin in an army vehicle in the northern Baghlan province.