"Fourteen children were amongst those killed, and one was an Afghan National Army soldier," Nato's International Security Assistance Force (Isaf) said in a statement.
Abdul Rahman, a doctor at a hospital near the blast, said the children were between the ages of eight and 10.
US General David McKiernan, the senior Nato commander in Afghanistan, said he believes the attack was carried out by a follower of Sirajuddin Haqqani.
Sirajuddin Haqqani and his father, Jalaluddin Haqqani, are regional commanders thought to be based in Pakistan's northern Waziristan region.
A suspected US drone aircraft targeting the two men fired on the town of Miranshah in North Waziristan in September, killing 23 people, including eight children.