Police said in comments carried by the official Saudi Press Agency today that the officer was killed late the previous night in the village of al-Jish.
The community is located in the eastern Qatif region, which is the heartland of Saudi Arabia's Shiite Muslim minority and was the site of deadly bombing at a Shiite mosque in May that was claimed by an Islamic State group affiliate.
Saudi Shiites have long complained of discrimination in the Sunni-ruled kingdom.
Two suspects have been arrested in connection with the shooting.