Authorities also imposed a curfew in parts of the region's main city of Srinagar, where hundreds of police and paramilitary troops patrolled deserted streets and erected checkpoints to halt any protests.
Seven killed in gun battle in Indian-held Kashmir
"No one is allowed to leave their home. There are soldiers everywhere," Umar Ahmed, a student, told AFP by phone from his home in Srinagar's old quarter.
Businesses closed throughout the region after separatist leaders, placed under house arrest to prevent them leading protests, called for a strike, while Kashmir University cancelled student exams.
Authorities also suspended train services in the region to stop protesters gathering.
Indian army kills four near border in Kashmir
A female university student was killed on Sunday as troops cordoned off Kakpora village, 35 kilometres south of Srinagar, suspecting the presence of militants.
Police say she was caught in crossfire between troops and militants after stone-throwing villagers gathered in support of the rebels.
A teenage boy also died after being hit by a tear-gas canister.
Witnesses say soldiers fired on the protesters, killing the woman who was standing outside her home. Other protesters were taken to hospital with gunshot wounds, they say.
Suspected separatists kill three soldiers in Indian Kashmir
Militants fighting against Indian rule of the Himalayan territory have wide support among Kashmir's Muslim residents, who often gather on the streets to protest during rebel gunbattles with government forces.
Since 1989 several rebel groups have been fighting Indian soldiers deployed in the territory, demanding either independence or a merger of the region with Pakistan.
The fighting has left tens of thousands, mostly civilians, dead.
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