Spokesman for the provincial police Khalil Asir said the mine detonated in the northeastern province of Takhar, killing the children, who were nine to 12 years old, included four from what Asir described as a "Taliban family".
"This area is under Taliban control and since security forces launched attacks to clear it, the Taliban have planted anti-personnel mines," Asir told Reuters.
"Unfortunately, today, one of those mines exploded and killed nine primary school students," he said.
Civilian casualties have been increasing to record levels this year, despite US-Taliban peace talks.
A record 4,313 civilians were injured or killed between July and September, a 42 percent increase from the same period last year, the UN Assistance Mission in Afghanistan said last month.
The toll included more than 1,000 deaths, the bloodiest period since the mission began collecting figures in 2009. It brought the number of civilian casualties for the first nine months of the year to more than 8,000.