"Curfew has been imposed as a preventive measure to maintain law and order in these areas," a police officer said.
Contingents of police and paramilitary Central Reserve Police Force (CRPF) in riot gear have been deployed to enforce the restrictions in the affected areas.
Traffic intersections and main roads have been barricaded by coils of concertina wire.
"Since today (Thursday) morning no untoward incident has been reported from anywhere in the city," the officer added.
There was tension even in areas not under curfew as reports of the clashes spread. Authorities have also mounted vigil in other towns and villages of the Kashmir Valley with a mix of Shia-Sunni population.
Educational institutions, banks, post offices, businesses and other routine activities were also affected.
The Kashmir University has postponed all the examinations scheduled on Thursday.