The 105-year-old Islamia Higher Secondary School in downtown Srinagar was set ablaze on Monday in a suspected arson attack that police blamed on Muslim rebels fighting Indian rule.
The fire also destroyed about 30,000 books and a rare handwritten manuscript of the Quran.
The strike on Tuesday called by the chief imam of Kashmir, Mirwaiz Umar Faruq, whose Awami Action Committee ran the school, closed down most educational institutions in the city.
"I believe it is the handiwork of the same forces who eliminated my uncle Moulvi Mushtaq. We know them closely and shall expose them shortly," Umar Faruq, who is also a top leader of the main separatist alliance All Party Hurriyat Conference, told the Greater Kashmir newspaper.
Moulvi Mushtaq Ahmad, an uncle of Umar Faruq, died in an attack by suspected rebels last month.
Umar Faruq was part of a moderate group of Hurriyat leaders who started talks with Indian government leaders in January, for the first time since an uprising broke out in 1989 against New Delhi's rule. Armed fighters opposed the talks.
A fresh wave of rebel violence has engulfed Kashmir despite peace moves by India and Pakistan, which agreed last month to a sustained dialogue for a final settlement of their dispute over the Himalayan region.
Violence in the first five days of this month has killed at least 50 people and wounded more than 70, police said.