Additional Superintendent of Police Mubashir Bukhari was injured in the stomach during stone pelting at Janglat Mandi in Anantnag district, a police official said.
A constable was injured during clashes with protesters at Hyderpora chowk in the outskirts of the city, the official said.
Four persons including a photojournalist with a local magazine were injured in clashes at Safakadal near Eidgah in the city as security personnel fired pellet guns and tear smoke shells to disperse the stone-pelting mob, the official said.
All the injured have been admitted to nearby SMHS hospital, he added.
Situation in rest of the Valley is stated to be normal, the official said.
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, he said.