All examinations scheduled for Monday have also been postponed.
Internet services were suspended in Shopian, Kulgam and Chadoora areas while train services between the valley and Jammu’s Bannihal town were cancelled.
The victims, Owais Ahmad Dar and Muhammad Sayeed Bhat, died after they were hit by pellets during clashes with the security forces in Kakapora and Shopian towns.
Clashes between stone pelting protesters and the security forces broke out in many south Kashmir areas after three militants including Yasin Yatoo, the operational commander of the Hizbul Mujahideen were killed in a gunfight in Shopian’s Awneera village earlier on Sunday.
Yatoo joined the banned outfit in 1997. He was the longest surviving militant commander in Kashmir.
Two soldiers were also killed in the gunfight.
Authorities have made heavy security deployments in Srinagar’s old city and uptown areas.
Officials have announced restrictions in areas falling under five police stations of Rainawari, Khanyar, Nowhatta, M.R. Gunj and Safa Kadal.