The incident took place at 12.40am (0710 GMT) in northern Baramulla town, 55km north of Kashmir’s summer capital Srinagar on Sunday.
Police said a constable from India’s Central Reserve Police Force (CRPF) opened fire on his colleagues after a fight broke out.
“Six CRPF personnel were killed and three others injured in the initial firing by an agitated policeman,” a police spokesman said, adding the gunman was shot dead by one of the injured policemen.
He said one of the injured died later in hospital while the condition of two others was critical.
Two of those killed were officers, one of whom had scolded the constable on Saturday over alleged indiscipline, the spokesman said.
The camp houses a battalion of the CRPF, which is gradually taking over counter-insurgency operations in Kashmir from India’s paramilitary Border Security Force and the army.
Indian troops, often under stress through working away from home for months without break, have been involved in similar incidents, most sparked by request for leave being denied.
Kashmir is in the grip of a 15-year-old conflict that has so far left 40,000 people dead by official count. Separatists opposed to Indian rule in the region put the toll between 80,000 and 100,000.