The blast Monday in the Malizi area of the province's Khairkot district occurred when one of the children stepped on the explosive device, Mukhlis Afghan, a spokesman for the governor, told Pajhwok Afghan News. Those injured were taken to a hospital, where some remained in critical condition.
There was no immediate claim of responsibility but the governor's spokesman said it was the handiwork of the Taliban, the report said.
Khaama Press also said local official blamed the Taliban as its insurgents frequently use similar explosive devices to target Afghan and coalition security forces.
CNN quoted the U.N. Assistance Mission in Afghanistan as saying in the first six months of this year, 231 children have died and 529 more were injured. The deaths and injuries largely were due to improvised explosive devices, including mines used by insurgent groups. The other main cause was the fighting between insurgents and Afghan forces.
Insurgent violence in Afghanistan has escalated as NATO and U.S. troops make preparations to end their combat operations by the end of 2014 and withdraw from the country.
Last weekend, a suicide bomb attack in the capital Kabul killed 10 people and injured 20 more, and the Taliban claimed responsibility for the attack. Those killed included a police officer.
The attack occurred near the Burhanuddin Rabbani University, where tribal leaders were scheduled to meet Tuesday to discuss a bilateral security agreement with the United States.