The Himalayan region's biggest mosque, the Jama Masjid, was ordered closed and people were only allowed to pray in smaller local mosques so that no big crowds could gather, witnesses said.
Occupied Kashmir has been in a security lockdown for eight days as India's Hindu nationalist government, led by Bharatiya Janata Party (BJP), seeks to snuff out opposition to its move to impose tighter central control over the region.
Internet and phone communications have been cut and tens of thousands of troop reinforcements have flooded the main city of Srinagar and other Kashmir Valley towns and villages.
Authorities had eased restrictions temporarily on Sunday to let residents buy food and supplies for Eid, one of the most important Muslim festivals of the year.
But security was tightened again after sporadic protests involving hundreds of people during the day, residents said. Police vans toured the streets late on Sunday telling people to stay indoors.
“I can't believe we are forced to be in our homes on this festival. This is the festival of joy and happiness,” resident Shanawaz Shah told AFP.
Too scared to eat
Indian-occupied Kashmir police chief Dilbagh Singh said people “have been asked to offer prayers locally”.
Singh insisted that occupied Kashmir was peaceful despite the protests.
“One incident in downtown Srinagar does not define the entire valley or the state,” he said.
Residents said the security crackdown had made them too fearful to celebrate.
A sheep trader at a Srinagar market, who gave his name as Maqbool, said the number of people buying animals for traditional feasts was sharply lower and he had gone from “huge profits” last year to a “big loss” this time.
Several thousand people took part in one rally after Friday prayers that was broken up with tear gas and shotgun pellets. But authorities denied there was any protest.
Prime Minister Narendra Modi has insisted the constitutional changes to occupied Kashmir are needed to bring peace and prosperity to a region blighted by a decades-old insurgency against Indian rule that has left tens of thousands dead.
He has won widespread backing in India for the move.
But local Kashmiri leaders say that stripping the region of its autonomy risks worsening the unrest.
Many Kashmiri political leaders have been detained and Indian media reports said some had been taken to detention centres outside the state.
Fury in Pakistan
India's move has also sparked fury in Pakistan, which insists that Kashmiris be given their right to self-determination.
The neighbours have fought two wars over the Himalayan region which they split after their independence in 1947.
In a series of tweetson Sunday, Prime Minister Imran Khan compared India's tactics in occupied Kashmir to those of the Nazis.
The premier said the Rashtriya Swayamsevak Sangh's (RSS) “ideology of Hindu Supremacy, like the Nazi Aryan Supremacy, will not stop” in the occupied region. He also compared the autonomy move as “the Hindu Supremacists version of Hitler's Lebensraum”. RSS is said to the parent organisation of the ruling BJP.
Officials said Prime Minister Imran would visit Azad Jammu and Kashmir this week to show solidarity.
Pakistan has already expelled the Indian ambassador, halted what little bilateral trade exists and suspended cross-border transport in protest at New Delhi's decision to revoke Article 370 of India's constitution.
Tensions remain fraught in occupied Kashmir's mountainous Ladakh region, where a local activist told AFPdozens of protesters took part in rallies on Thursday, Friday and Saturday, with at least 10 people injured by security forces using tear gas and batons.
Modi insisted last week the decision to strip occupied Kashmir of its autonomy was necessary for its economic development, and to stop “terrorism”.
Under its previous constitutional autonomy, Kashmiris had special privileges such as the sole right to own land or take government jobs and university scholarships.