Clashes took place in Safakadal near Eidgah in Srinagar and in Hyderpora on the outskirts of the city after the Eid prayers, police said.
Parts of Anantnag district and Sopore town in north kashmir's Baramulla district also witnessed clashes after the prayers, a police official said.
Additional Superintendent of Police Mubashir Bukhari was injured when he was hit by a stone in the stomach during stonepelting at Janglat Mandi in Anantnag district, the official said.
Eyewitnesses said more than dozen protesters sustained injuries in the police action amid claims that even ordinary civilians were targeted while dealing with protesters.
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Photographs showing security personnel purportedly vandalising private vehicles went viral on social networking sites like Facebook and Twitter in the aftermath of the clashes.
However, police officials said the forces exercised maximum restraint while dealing with the unruly mobs.
One cop was critically injured when he was hit by a pellet accidentally fired from his own gun, the official said.
All the injured have been admitted to hospitals, he added.
Situation in rest of the valley was reported to be normal, the official said.
The authorities had placed top separatist leaders including Syed Ali Geelani, Mirwaiz Umar Farooq and Mohammad Yasin Malik under house arrest, fearing their presence at large Eid gatherings could spark violence.