Police took action after hundreds emerged from mosques and held noisy anti-India demonstrations in Srinagar, the main city in the region, chanting "Go India! Go back!" and "We want freedom!", witnesses said.
The protesters retaliated by hurling stones at the police.
In the southern district of Anantnag, a similar clash occurred after police prevented worshippers from taking part in a rally to protest against Indian occupation in the region, resident Ghulam Hassan told AFP by telephone.
The holiday is being celebrated in a low-key manner in Indian Held Kashmir after months of curfews and violent clashes between protesters and the security forces. A total 111 people have died since June.
Authorities deployed thousands of troops in Srinagar to prevent a repeat of massive protests that hit the city two months ago on Eidul Fitr.
The commercial Lal Chowk area, where protesters hoisted Islamic and Pakistani flags during the last holiday, was sealed with barbed wire.
Key leaders Syed Ali Geelani, Mirwaiz Umar Farooq and Shabir Shah were placed under house arrest, police said.
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