Attacks, some claimed by the Pakistani Taliban, have risen, mostly targeting police and security officials
The militants fired at Waseem Bari, a former district chief of the BJP, and his father and brother while they were in their shop in Bandipora district in north Kashmir, police said. All three died in hospital later.
Prime Minister Narendra Modi's BJP-led government last year revoked Muslim majority Kashmir's special autonomy in order to cement its grip over a region that has faced years of militancy and unrest.
Militants have vowed to fight the change.
All 10 security guards of the BJP leader were arrested after the attack, said Kashmir Police Chief, Vijay Kumar.