The areas placed under restrictions fall under Rainawari, Khanyar, Nowhatta, M.R.Gunj, Safa Kadal, Kralkhud and Maisuma police stations.
Restrictions have also been imposed in Handwara and Kupwara towns of Kupwara district and Pulwama town in south Kashmir.
Heavy deployment of police and paramilitary central reserve police force (CRPF) has been made at sensitive areas here and all other district headquarters of the Valley.
The restrictions come after separatist leaders, including Syed Ali Geelani, Mirwaiz Umer Farooq and Muhammad Yasin Malik, called for protests against the killings of four people by security forces in Kupwara district.
Chief Minister Mehbooba Mufti, who arrived here on Thursday, has directed security forces to strictly follow the SOP (standard operating procedure) during crowd control operations so that no civilian is harmed.