The explosion also injured 14 passers-by. Residents told AFP by telephone that the attack sparked panic and damaged at least one vehicle.
Six members of the federal Central Reserve Force (CPRF) were hurt in a grenade blast triggered in the village of Gagran, about 50 kms south of the state's summer capital, Srinagar.
"A solo militant hurled a hand grenade at a CPRF patrol which exploded with a bang sending splinters in all directions," the spokesman said.
In a separate attack, one policeman died and four were injured when a suspected fighter hurled a grenade at a police post in Surankote, in the Poonch border district, 210 kms west of the winter capital Jammu, according to an Indian police spokesman.
The suspected rebel arrived at the entrance of the post, pulled out a grenade and lobbed it at the policemen before escaping.
In further violence in the restive state, a solider was killed overnight and an officer injured in an ambush carried out by separatists using AK-47 rifles and guns southern Kashmir's Rajouri district, Indian police said.
The presence of Indian troops has
confined children indoors
Today's attack followed a day of reported bloodletting by Indian troops. Kashmiri news sources said 18 civilians were killed in a single incident in the Gurez area of Baram Allah district.
The Indian army claimed yesterday that it had shot dead 15 "militants". The account was disputed by the pro-independence Kashmir Media Service which said troops had in fact gunned down 18 civilians.
Neither claim could be independently verified.
According to India, more than 38,000 people have died in the disputed state since an anti-Delhi insurgency uprising erupted in 1989. Separatists put the toll at between 80,000 and 100,000.
The majority-Muslim state is fighting for India to implement UN resolutions calling for a plebiscite on whether its people want to stay in India or accede to Pakistan. India has always ruled out the possibility of holding a plebiscite.