The explosion on Wednesday took place in the Nowgam area on the outskirts of the summer capital, Srinagar.
The bomber was among those killed in the attack.
"The initial reports indicate a suicide bomber died in the attack," a police spokesman said. "Two other people also died ... . More than 12 people were injured including five policemen."
The Muslim group Jaish-e-Mohammed immediately claimed responsibility for the blast in a telephone call to local news agency Current News Service (CNS).
"Our suicide bomber targeted a security patrol," the spokesman for the group told CNS.
The explosion came just hours before the scheduled swearing-in ceremony of Ghulam Nabi Azad as the Himalayan state's new chief minister.
The switchover is part of a power-sharing deal between regional Peoples Democratic Party (PDP) and Azad's Congress party. PDP's Chief Minister Mufti Mohammed Sayeed completed his three years in power on Wednesday.
The already-tight security for the swearing in ceremony at the International Convention Complex was beefed up, a police officer said.
The car blast follows serial bombings at the weekend in New Delhi which killed 62 people in crowded market places.