The officer was killed in a restaurant in Constantine by three gunmen who shot him and ran away with his service weapon.
The army acknowledged the officer was killed by a terrorist group but could not name it. A hunt for the suspects has been under way in the district since Sunday.
IS news agency Amaq claimed IS fighters shot the officer and seized his weapon in the attack on Friday in Constantine, 400 kilometers east of the capital Algiers, the New Arab reports.
The group also released a picture of the stolen gun.
Algeria has been relatively spared by the group’s attacks. However early this month, the global terrorist group indicated that it was launching operations in the North African country.
IS came in the country following alignment of an off-shoot of al-Qaeda to the militant group in 2014.
In March the group attempted a suicide-bomb attack against a convoy of the Algerian army. The army claimed it killed the attacker.
Around 200 IS militants are reportedly present on Algerian soil.