-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.
Kashmir has been in a security lockdown for eight days as the Hindu nationalist government in New Delhi 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 celebrations 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 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
Kashmir police Chief, Dilbagh Singh, said people "have been asked to offer prayers locally".
Singh insisted that 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 had fallen sharply 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, which was disrupted using tear gas and rubber bullets. However, the authorities denied there had been any protests.
Prime Minister Narendra Modi has insisted the constitutional changes to Kashmir are needed to bring peace and prosperity to a region blighted by a decades-old insurgency against Indian rule, which has left tens of thousands dead.
He has won widespread backing in India for the move.
But local leaders in Kashmir say that stripping the region of its autonomy risks worsening the unrest.
Many political leaders in Kashmir have been detained and Indian media reports show some had been taken to detention centers outside the state.
Fury in Pakistan
India's move has also sparked fury in Pakistan, which also claims Kashmir as it own territory.
The neighbors have fought two wars over the Himalayan region, which they split after their independence in 1947.
In a series of tweets on Sunday, Pakistan Prime Minister, Imran Khan, compared India's tactics in Kashmir to those of the Nazis.
Khan said the "ideology of Hindu Supremacy, like the Nazi Aryan Supremacy, will not stop" in Kashmir.
He also compared the autonomy move as "the Hindu Supremacists version of Hitler's Lebensraum".
Officials said Khan would visit the Pakistan-controlled part of Kashmir this week in a show of solidarity.
Pakistan has already expelled the Indian ambassador, halted what little bilateral trade exists and suspended cross-border transport in protest to New Delhi's move on Kashmir.
Tensions remain fraught in Kashmir's mountainous Ladakh region, where a local activist told AFP dozens 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 Kashmir of its autonomy was necessary for its economic development, and to stop "terrorism".
Under its previous constitutional autonomy, Kashmiris enjoyed special privileges, such as the sole right to own land, take government jobs and receiving university scholarships.
With Kashmir now fully part of the Indian union, Modi said the region would enjoy more jobs and less corruption and red tape, adding that key infrastructure projects would be expedited.