Bhat, who succeeded Burhan Wani, was killed along with another militant in an encounter with security forces in Tral area of Kashmir's Pulwama district.
Soon after the killings, stone-pelting protests started at around 50 places, including Tral in Pulwama and Khanabal in Anantnag in south Kashmir, the police said.
A person in Mattan area in the district was injured during clashes with security forces, they said.
The situation across the Valley is tense. Unnerved people rushed to their homes, leading to traffic snarls on certain routes. The schools also closed three hours early.