The 201st Silab Corps of the Afghan National Army (ANA) forces said the incident took place on Saturday evening in Dangam district.
The incident took place as the militants were transporting an artillery shell that went off on the way, the 201st Silab Corps said, ad ding that 5 more civilians were wounded.
The Taliban militants group has not commented regarding the report so far.
Kunar is among the relatively volatile provinces in eastern Afghanistan where the anti-government armed militant groups including the Taliban insurgents and foreign militants including the loyalists of the Islamic State of Iraq and Syria (ISIS) terrorist group are actively operating in a number of its districts.
The Taliban group in Afghanistan is accused of incurring the most of casualties to the civilians as the group’s insurgency entered to its 15th year.
The United Nations Assistance Mission in Afghanistan released the latest civilian casualties report late in July which stated at least 3726 civilians were killed or wounded between January and June of this year.
The UN mission said the civilian casualties in the country has reached to a record number since counting began in 2009, with 5,166 civilians recorded killed or maimed in just the first six months of this year, of whom almost one-third were children.
The total civilian casualty figure recorded by the UN between 1 January 2009 and 30 June 2016 has risen to 63,934, including 22,941 deaths and 40,993 injured.
According to the UN mission, the anti-government elements remain responsible for 60 percent of the civilian casualties with ground engagements continuing to cause the highest number of civilian casualties, followed by complex and suicide attacks and improved explosive devices (IEDs).