Fire at the higher senior secondary school broke out in the afternoon. It was doused by fire engines along with the help of locals, an official said.
A Jawahar Navodya Vidyalaya school in Aishmuqam was also set on fire on Saturday night.
Officials said the cause of fire in both incidents has not been ascertained yet.
Schools in Kashmir valley have been closed due to a shutdown call by separatist groups. Dozens of schools are also still occupied by security forces brought here to contain the unrest, which began after the 22-year-old Hizbul Mujahideen terrorist Burhan Wani was killed on July 8.
Opposition leader and former Chief Minister Omar Abdullah called for "strictest punishment" for the people behind the incidents and blamed both the government and separatist for "failing to speak up and act in time" to prevent such incidents.
"Robbing our children of their classrooms and of the prospects of academic growth is the greatest act of tyranny and oppression," the National Conference leader said.
Officials say more than 12 lakh students are unable to go to school for the last four months in Kashmir as the education has become a new flashpoint during current unrest.