Mawlawi Mushtaq was one of several politicians who favoured a peaceful political resolution to the half-century-old dispute over the Himalayan region.
He was also the uncle of Kashmir’s chief Muslim cleric and leader of Hurriyat Conference, an alliance of separatist parties.
Mushtaq was buried at an ancestral graveyard in Srinagar’s Malkhah neighbourhood.
Many mourners chanted pro-freedom and pro-Pakistan slogans, vowing to avenge the killing of the 61-year-old cleric.
Mushtaq died on Monday evening, about 10 days after being shot at several times by an assailant inside a mosque on 29 May.
Neither Indian or Pakistani security officials have been able to confirm who was responsible for the attack.
A complete shutdown is being observed in Srinagar, a city of more than a million people, and most other parts of the Valley of Kashmir.
Islamist resistance movement al-Umar Mujahidin also called for a general strike to pay homage to Mushtaq.
Hundreds of armed policemen and paramilitary troopers have fanned out across the city and other main towns to maintain order.
On Monday, Srinagar witnessed sporadic violence by protesters, forcing traders to suspend work and stop traffic.