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Suspected rebels lobbed a grenade at a group of police and paramilitary troops in the main city of Srinagar following protests against Modi's visit.
"Four personnel of CRPF and seven policemen were injured in the grenade blast," Bhuvesh Choudhary, spokesman of the paramilitary Central Reserve Police Force (CRPF) said.
One of the police officers who was wounded in the blast later died of his injuries, inspector general Javid Gillani told AFP.
Armed encounters between security forces and rebels fighting to end Indian rule over Kashmir have become more frequent since massive protests last year, sparked by the killing in July of a popular militant leader.
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Large parts of the Kashmir valley observed a virtual shutdown Sunday following a call by separatists protesting Modi's visit.
At a rally, Modi urged Kashmiri youth to choose "tourism over terrorism", inaugurating an 11-kilometre (seven-mile) tunnel across the Himalayas intended to ease travel in the disputed region.
"This bloody game could not do any good to anyone during the last forty years," he said.
The two-lane road tunnel, India's longest, will cut the travelling distance between the region's two main cities of Jammu and Srinagar by 41 kilometres (25 miles), bypassing stretches that often shut due to heavy snowfall and landslides.
Kashmir has been divided between India and Pakistan since the end of British rule in 1947. Both claim the Himalayan territory in its entirety.
Rebel groups have for decades fought roughly 500,000 Indian soldiers deployed in the region, demanding independence or a merger of the territory with Pakistan.
The fighting has left tens of thousands, mostly civilians, dead.