According to local government officials, the incident took place in Chapa Dara district earlier today.
Provincial police chief Abdul Habib Syed Kheli confirmed that a woman and her three children were killed and five others were wounded in the attack.
He said the incident took place after a group of Taliban insurgents launched an attack on the Afghan security forces check post.
Syed Kheli further added that the dead bodies of a number of Taliban insurgents were also left in the area who were killed during gun battle with the security forces.
The Taliban militants group has not commented regarding the incident so far.
Kunar is among the volatile provinces in eastern Afghanistan where anti-government armed militant groups are actively operating and frequently carry out insurgency activities.