Soon after polling started on Monday, suspected separatists hurled a grenade outside a polling station in Palhalan village, about 40km north of Srinagar, the summer capital of Jammu-Kashmir.
Police and witnesses said that suspected Muslim fighters tossed a hand grenade into a stationery van of India's Central Reserve Police Force (CRPF) at Khanyar in downtown Srinagar.
The vehicle caught fire and four policemen standing beside it were injured. Five pedestrians also sustained splinter injuries and, according to a witness, one of them died minutes after being hit.
Reyaz Ahmad, a police officer said that voting was not disrupted.The attack came despite tight security with thousands of troops patrolling the streets and guarding the 400 polling stations.
Nearly 300,000 voters were expected to vote to fill four seats in the 81-seat state legislature. One seat fell vacant after the incumbent was killed in an attack, one because of a resignation and two due to defections.
Voting was thin in the early hours because of the threat of attacks by separatists. Security forces searched the few voters queuing up outside polling centres.
Among those contesting is the chief minister, Ghulam Nabi Azad of the Congress party, which rules the Himalayan state in coalition with the People's Democratic Party.
Azad took office on November 2 under a power-sharing arrangement that calls for leaders of the two parties to take turns to hold the top elected office in the state.
Under the constitution, Azad had six months to be elected to the state assembly to confirm the post.
The PDP-Congress alliance came to power in 2002. Separatist violence reduced noticeably in the last three years when the PDP's Mufti Mohammed Sayeed was the chief minister.
The Congress has given assurance that it will maintain Sayeed's policies credited with reducing violence.
About 67,000 people, mostly civilians, have been killed in the 15-year insurgency by Muslim separatists fighting for the Indian Kashmir region's independence or merger with mostly Muslim Pakistan.
Yusuf Jameel contributed to this article from Srinagar