The officer was shot as he was leaving a mosque after prayers on one of Islam's holiest days.
"Suspected militants fired three bullets from close range at Muhammad Amin Bhat while he was exchanging Eid greetings outside the Barzulla Mosque," a police officer said in Srinagar city.
Bhat, a deputy inspector general of police, was declared dead on being taken to a hospital in Srinagar. His bodyguard was wounded, the police officer said.
Muslims in India were celebrating Eid al-Adha on Monday.
No group has claimed responsibility for the attack, which took place a day after authorities in Kashmir freed 34 prisoners and announced new incentives to persuade fighters to give up the gun.
On Sunday, 16 people were wounded when suspected fighters threw a grenade into a crowd at a marketplace in Pulwama district, south of Srinagar, police said.
Violence has continued in the Himalayan region despite a recent thaw in relations between India and Pakistan who have fought two of their three wars over the region since independence from Britain in 1947.
India accuses Pakistan of fomenting violence in Kashmir, where more than 40,000 people have been killed since 1989. Pakistan denies the charges.
Armed separatist groups have opposed the peace moves between India and Pakistan and vowed to continue attacks in Kashmir.