Police fired tear gas and used batons to ward off protesters who were chanting anti-India and pro-freedom slogans, witnesses said.
Security forces moved in after hundreds of worshippers, mostly youths, streamed out of mosques and held noisy demonstrations in the towns of Anantnag and Sopore.
Protesters retreated into narrow lanes and pelted police and paramilitary forces with stones, sparking the violence.
At least four policemen and three protesters were injured, a police officer said, asking not to be named as he was not authorised to talk to the media.
Eid al-Adha, or the Feast of Sacrifice, honours Abraham`s willingness to sacrifice his son Ishmael on the order of God, who according to Islamic tradition provided a lamb in the boy`s place.
Authorities deployed thousands of police and paramilitary in the summer capital Srinagar to prevent a repeat of the violent protests that hit the city last year on the Muslim holiday of Eid al-fitr.
Senior separatist leader Syed Ali Geelani had been placed under house arrest, his office said.
India has an estimated 500,000 troops in Kashmir, which is split into Indian- and Pakistani-administered parts. There has been a separatist insurgency in the Indian zone for 20 years that has left thousands dead so far.
In Srinagar and other towns people joined religious congregations in new clothes. Some children let off fire crackers and others played with toy pistols and toy rifles. (*)