Security is tight across the region, where thousands of extra paramilitary troops have been deployed during local elections, which are being held in five stages.
The killing occurred late Sunday, the day after a grenade attack injured eight people near a paramilitary bunker in Srinagar, the main city of the disputed region which is also claimed by Pakistan.
Police said Abdul Rashid Bhat, an elected leader of Nazneenpora village, 60 kilometres south of Srinagar, died on the spot.
"He was intercepted by militants outside his house and shot dead," superintendent of police Wahid Shah told AFP.
Turnout was high for the first phase of voting last Tuesday, when more than 70 per cent of the electorate cast their ballots in 15 constituencies.
The state of Jammu and Kashmir will vote in five phases, with results due on December 23.
Indian Prime Minister Narendra Modi's Bharatiya Janata Party (BJP) is staging a bold attempt to seize control of the Jammu and Kashmir legislature, a move unthinkable until very recently.
The Hindu nationalist party has traditionally had no base in the Kashmir Valley, where residents' resentment against Indian rule runs high.
About a dozen rebel groups have been fighting Indian forces since 1989 for independence or to merge the territory with Pakistan. The fighting has left tens of thousands dead, mostly civilians.
Most separatist leaders opposed to Indian rule, who have called for boycott of the polls, were either arrested or confined to their houses after elections were announced.
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@AG: Because they are supporting those rebels. Was it that difficult to understand?
Mr LS, AG's question was rhetorical. Was that that difficult to understand?
@AG: Because they are supporting those rebels. Was it that difficult to understand?
If you call Militants as Rebels then why don't you call the same for Balochistan??