The biggest mosque in Kashmir, namely, Jamia Masjid, was closed down and people could only gather in small groups to pray.
Worshippers were encouraged to attend prayers in the areas where they lived rather than try to go to Srinagar’s best-known mosques.
Frustration is growing in Muslim-majority Kashmir over India’s move last week to curtail autonomy for the state of Jammu and Kashmir, including a bar on non-residents buying property.
Hundreds of people shouting anti-India slogans spilled on to the streets following prayers in the neighborhood of Soura, the site of a big demonstration Friday, but authorities largely sealed off the area and kept the protest localized.
"We want freedom, we are neither a part of India, nor Pakistan," said Asifa, an 18-year-old woman who was among those protesting after prayers at the shrine of Jinab Sahib in Soura.
"Modi is lying to his people that the removal of special status of Kashmir is good for us," she said. "We will resist it till our last breath."
The clampdown on communications remained in place for an eighth day, with no regular Internet, cell phone or fixed-line links working. Virtually no independent information has emerged from elsewhere in the Kashmir Valley but Srinagar over the past week.
More than 300 regional leaders and activists remain in various forms of detention.
Many women were among the people seen breaking down in tears amid chants of "We want freedom" during the prayers.
On Monday, there were few signs of festivities, with many Srinagar residents saying they planned to skip the usual ritual of animal slaughter as they did not feel like celebrating.
"What are we celebrating? I can’t call my relatives to wish them Eid, we can’t go out to buy things. So, what kind of celebration is this?" asked Aneesa Shafi, an elderly woman entering a mosque in the city's Barzulla area.
Activists gathered in India’s capital city Delhi to mark Eid with fellow Kashmiris who have no contact with their families. Almost 300 people gathered to mark the holiday.
"I am here to express my solidarity with the people of Kashmir who have not been able to go home and are not able to talk to their parents because there is a total clampdown on communication," said activist Shabnam Hashmi. "We are not celebrating Eid today."