The boy, who lived in Hayan village of the district, was playing when he was attacked by the big cat, a police spokesperson said.
A group of villagers raised an alarm and chased the leopard, which managed to escape into the nearby forest, he said, adding that the boy was taken to a nearby hospital where he was declared brought dead.
Attacks by wild animals on human beings have increased across Kashmir Valley over the past couple of months, leaving seven persons, including four children, dead.
On May 24, Forest Minister Mian Altaf had said the government was planning to introduce a low-cost methodology using organic fencing to check increasing cases of man-animal conflicts in the state.