The killings came on a night of violence in which suspected opposition groups also shot dead a woman and two of their own colleagues, while Indian troops gunned down three fighters.
A police spokesman said armed men barged into the house of Mohammed Shafi in southern Rajouri district and beheaded him. His son and daughter, Liyaqat and Zarina, were also beheaded minutes after their father’s killing.
The killings sparked panic in the remote area.
No group has claimed responsibility. Police believe the three were killed on suspicion of working for Indian troops.
In the Marood area of Rajouri district, Indian troops shot dead three rebels during a fierce gun fight overnight, police said, adding two security force personnel were injured in the fighting.
In southern Doda district, suspected rebels shot dead a Muslim woman overnight after accusing her of being a police informer, police said, adding two men died in inter-group rivalry in the same district.
Police said the reason for the group rivalry was not immediately known and that they were investigating.
Thousands of people have died in Kashmir since the eruption of an anti-Indian insurgency in the region 15 years ago.