The attack happened while the police vehicle was passing through a crowded market in the Batamaloo area of the state capital Srinagar.
"It was a random attack on police. A militant who was being shifted to a jail was also badly injured in the head," police official Afadul Mujtaba told AFP.
No arrests have been made over the attack, Mujtaba said.
Kashmir is divided between India and Pakistan by a UN-monitored boundary known as the Line of Control. But both countries claim the Himalayan region in full and have fought two of their three wars over the territory.
Armed violence in Kashmir has declined during the last decade but recent months have witnessed more attacks by separatist militants on Indian forces.
On June 24 heavily armed rebels ambushed an army convoy and killed eight soldiers on the outskirts of Srinagar, on the eve of a rare high-profile visit to the region by Indian Prime Minister Manmohan Singh.
About a dozen armed rebel groups have been fighting Indian forces in Kashmir since 1989 for independence or merger with Pakistan. The fighting has left tens of thousands, mostly civilians dead.
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Kashmir is Indias permanent part