They say the attacker was targeting a passing US military patrol but it was unclear if there were any American casualties.
Gen Zelmia Oryakhail, provincial police chief of Paktia province, said the bomber was on a motorbike and detonated his explosives at midday today outside the market in Samkani district as the American forces passed.
He said a local school had just let students out for lunch.
He said 15 other students were wounded. He did not say how old they were.
The international coalition didn't immediately confirm the incident.