According to the local security officials, the incident took place after an explosive device planted in the vehicle of a Provincial Council member went off.
The anti-government armed militant groups including the Taliban insurgents have not commented regarding the report so far.
Laghman is among the relatively peaceful provinces in eastern Afghanistan but the anti-government armed militant groups are active in a number of its remote districts.
The Afghan intelligence operatives thwarted a coordinated suicide attack plot by the Taliban militants group in Mehtarlam city last week.
The National Directorate of Security (NDS) said a group of three terrorists belonging to Taliban group were arrested before they manage to carry the attack in the city.
According to a statement by NDS, the group was looking to carry out the attack by initially detonating a rickshaw packed with explosives and a magnetic bomb.
Earlier, a famous commander of the Taliban group was killed in an ambush by the Afghan Local Police (ALP) forces in Alisheng district of Laghman province.