Police opened fire and used tear gas to disperse the crowds, but the news of the death brought more protesters onto the streets of the city of Srinagar.
The area was in a security lockdown during Mr Modi's visit.
Kashmir, claimed by both India and Pakistan in its entirety, has been a flashpoint for more than 60 years.
The two South Asian rivals have fought two wars over the region in the Himalayas.
During his one-day trip, Mr Modi steered clear of discussing politics.
Instead, he focused on an aid package to the region, promising $12bn (Â£8bn).
Mr Modi expressed hopes that his could "change the fate of Kashmir".
"I want to build a new Kashmir, a powerful Kashmir," the prime minister said.
But several separatist leaders warned that a political problem could not have an economic solution.
"PM Modi has made the same mistake of weighing the Kashmir issue in rupees," said Omar Abdullah, the former chief minister of the state.
A demonstrator has been killed in clashes with government troops in Indian-administered Kashmir, following a visit there by PM Narendra Modi.