They said the strike on the madrassa in the village of Hazara Qurluq killed 11 children and their prayer leader.
The Afghan government disputed the account, saying it had killed 12 Taliban fighters in the village.
The strike came after more than 30 security force members were killed in a major Taliban ambush in the province.
Local officials said 14 others were wounded in the strike late last night. The imam of the mosque attached to the seminary, Abdul Awal, who was among the wounded and was admitted to hospital, told the BBC that only he and children were in the mosque at the time of the strike.