Police officers and witnesses said on Sunday Umar Abd Allah, leader of the National Conference party and a former Indian junior foreign minister, was unhurt in the blast.
His father, Faruq Abd Allah, former chief minister of Indian-administered Kashmir, also escaped unhurt but two other mourners were seriously wounded.
"I heard two civilians screaming while lying in pools of blood after the explosion," witness Tariq Ahmad from Sarnal in Anantnag district said.
"It was a remote-control type of bomb," a police official at the scene said.
No group has claimed responsibility for the second attack on senior National Conference leaders in the past four days. On Thursday, anti-government fighters killed Safdar Baig as he was coming out of a mosque after prayers.
Plume of dust
TV footage on Sunday showed police security guards ducking behind cars after the explosion, which sent up a big plume of dust and debris, and then opening fire in the air.
Policemen were also shown carrying one of the wounded in a white sheet.
"They (the federal) government is playing with our lives. New Delhi must open its eyes to the situation here," Umar Abd Allah said in Sarnal.
Indian security forces have been
battling separatists since 1989
He was among the mourners who had gathered to attend Baig's funeral. Witnesses said Umar Abd Allah was about three metres from the site of the blast.
Separatists have been waging an armed campaign against New Delhi's authority since 1989.
Jammu and Kashmir is India's only Muslim-majority state.
More than 40,000 of people have been killed in the revolt in the state. Separatist groups put the toll twice as high.
The region has been the cause of two out of three wars between India and Pakistan, which controls a third of the Himalayan region of Kashmir.
The scenic region is the main sticking point in peace talks between the nuclear-armed neighbours, which are pursuing a peace process started last year.