Tension had been building ahead of the anniversary with three civilians, including a teenage girl, killed during clashes on Saturday between protesters and Indian troops.
Mobile internet services were shut down across Indian-administered Kashmir, roads into the restive valley were blocked and restrictions on movement were imposed in Srinagar.
Authorities have clamped a total curfew in Tral, the native home of rebel commander Burhan Wani.
The charismatic young leader's death in 2016 sparked months of violent street protests that left nearly 100 dead and countless more blinded by pellet fire following an Indian crackdown.
Separatist leaders urged shopkeepers to keep their businesses closed in protest to mark Wani's death.
Kashmir has been divided between India and Pakistan since the end of British colonial rule in 1947, but both claim the former Himalayan kingdom in full.
India has about 500,000 soldiers deployed to its half of Kashmir, where armed groups have for decades been fighting for independence or a merger with Pakistan.
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