The rebels also shot dead a man, his wife and three-year-old son overnight in a renewed burst of violence in the Himalayan territory at the heart of decades of tension between India and Pakistan.
The dead man was a member of the Ikhwan, a pro-India group helping security forces fight separatist rebels, police said.
Kashmir's chief religious leader, Maulvi Umar Faruq, was visiting a wounded relative in hospital on Saturday when a rifle grenade hit the top floor of his house in summer capital Srinagar and damaged windowpanes, a police officer said.
Earlier, a Pakistan-based militant group, al-Umar Mujahidin, claimed responsibility for an attack in another part of Srinagar that wounded Faruq's relative, Maulvi Mushtaq Ahmad, who is also a separatist leader.
Faruq, chief preacher of the main mosque in Srinagar, and top leaders of the main separatist All Parties Hurriyat Conference began talks in January with top Indian government leaders for the first time since a revolt broke out in Kashmir in 1989.
A new round of talks is due next month.
Separatist violence has been falling in Kashmir since India and Pakistan, who fought two wars over disputed territory, began a peace process last year.
India, which blames Islamabad for stoking the 15-year-old revolt in its only Muslim majority state, says guerrilla incursions from Pakistan-administered Kashmir have stopped.
Islamabad has insisted on talks to resolve the dispute.
More than 40,000 people have died in the conflict in the Himalayan region, according to official figures. Separatists put the toll at more than 80,000.