Authorities imposed the indefinite curfew ahead of a separatist rally planned for Monday, but thousands of people took to the streets in several areas in defiance of the order.
The biggest demonstration took place in Handwara, 75km north of Srinagar, Kashmir's summer capital, where Muslims charged that security personnel had desecrated the Quran, Islam's holy book. Authorities denied the charge.
In the past two weeks Kashmir has seen some of the biggest pro-independence demonstrations since a separatist revolt against New Delhi's rule broke out in the region in 1989.
The protests were triggered by a dispute with the region's Hindus over transfer of land to a Hindu shrine trust, bolstering separatist sentiments in Kashmir.
Separatist leaders plan to address a huge rally on Monday in Lal chowk in the heart of Srinagar, insisting they will not be deterred by the curfew. A three-day strike called by separatists in the region began on Saturday.
"In fact government is trying to target us. They killed Sheikh Aziz and scores of innocent people," hardline separatist leader Syed Ali Shah Geelani said. "Now they are trying to suppress our peaceful struggle."
Sheikh Aziz, a senior separatist leader, was among 23 Muslim protesters killed by police over the past two weeks. More than 500 people have been injured in clashes.
BEATINGS AND ARRESTS
On Sunday, several journalists were beaten up by police and three were hospitalised, an association of Kashmiri journalists said.
"Security personnel are abusing and beating journalists," Farooq Khan president of Kashmir Press Photographers Association said. "We strongly condemn this."
Geelani said more than two dozen activists of the region's main separatist alliance, All Parties Hurriyat (Freedom) Conference, had been arrested in overnight police raids.
Thousands of police and troops were patrolling the region's streets to enforce the curfew. Police vehicles with loudspeakers urged people to remain indoors.
On Saturday evening, hundreds of Muslims took to the streets in Srinagar carrying torches and shouting: "Go India go! We want freedom."
The land dispute began after the state government promised to give a forest tract to a Hindu trust that runs the cave shrine of Amarnath. Many Muslims were enraged, leading the government to rescind its decision.
That in turn angered Hindus in Jammu, where thousands have protested the revocation of the land order and criticised the government for "pandering to separatists".