Paramilitary forces fired bullets and shotgun pellets as people protesting against Indian rule stormed polling stations near Srinagar.
Separatist leaders had called for a boycott of the vote.
Muslim-majority Kashmir is at the centre of a decades-old territorial dispute between India and Pakistan.
Both countries claim Kashmir in its entirety and control different parts of it.
Why were they protesting?
Rebel groups in Indian-administered Kashmir have for decades called for either independence or a union with Pakistan.
These groups have rejected local elections and urged voters to boycott Sunday’s poll, which took place after a politician resigned over what he described as the “anti-people” agenda of the Indian government.
Election officials reported a voter turnout of just 6.5%.
The Indian government deployed tight security ahead of the polling, with 20,000 additional troops sent to the area.
Internet services were also shut down in an attempt to hold a peaceful poll.