This week marks the second time during the pandemic that the world's biggest Muslim-majority nation has celebrated the Feast of Sacrifice, which signals the end of the annual pilgrimage to Mecca.
Authorities have banned large crowds, including at traditional events that feature the sacrifice of livestock, and urged the public not to gather for acts of religious worship.
In the capital Jakarta and elsewhere, some heeded an official request not to go inside mosques but instead gathered to pray on nearby roads, while residents in Bandung laid out their prayer mats in narrow alleyways outside their homes.
Thousands of others in Banda Aceh assembled in close quarters outside the Baiturrahman Grand Mosque, where vendors hawked animal-shaped balloons to families.
President Joko Widodo appealed to Muslims to pray at home to mark Eid rather than risk infection at public gatherings.
"In the midst of the pandemic, we need to be willing to sacrifice even more," he said in a Monday television address.
"Put the interests of the community and others first." Virus cases shot up after millions travelled across the vast archipelago of nearly 270 million people at the end of the holy fasting month of Ramadan in May.
Indonesia has in recent days overtaken India and Brazil as a global Covid-19 hotspot and its daily death toll hit a record of 1,338 on Monday.
Cases have been topping 50,000 a day, around 10 times above the average figure in early June, as the highly infectious Delta variant ripples across the country.
Checkpoints have been set up on roads across Java and domestic flights are subject to tighter restrictions in a bid to stop people from travelling to see relatives.
The surge has overwhelmed hospitals in the capital Jakarta and across densely populated Java, sparking shortages in oxygen.
Patients have been turned away by medical staff or treated in makeshift tents set up in hospital parking lots, as more and more of the sick die at home.
Indonesia has recorded more than 2.9 million cases and nearly 75,000 deaths but testing and tracing rates are low and experts believe the true figure is far higher.