According to local government officials, the incident took place late on Friday night after a motar round fired by militants landed on a residential house.
Provincial governor spokesman Sarhadi Zwak said the incident took place in Alingar district.
Zwak further added that the victims were members of a single family which included four women and eleven others including children were injured.
No group including the Taliban militants has so far claimed responsibility behind the incident.
Laghman is aong the relatively volatile provinces in eastern Afghanistan where anti-government armed militants are actively operating in a number of its districts and frequently carry out insurgency activities.