Corporal Khalaf al-Harithi was on duty at a station in the western region on Thursday evening when he was hit by gunfire from an unknown source, the ministry said in a statement.
An investigation is under way into the incident.
It occurred several hours after officers shot dead two "terrorists" during an exchange of fire at their hideout between the holy city of Mecca and the mountain resort of Taif, about 80 kilometres to the east, according to the ministry.
A simultaneous raid occurred on a hideout in the Red Sea city of Jeddah, where two people were arrested.
Since late 2014 the Islamic State group of Sunni extremists has claimed deadly bombing and shooting attacks against the kingdom's minority Shiite community, and members of the security forces.
Abu Bakr al-Baghdadi, leader of the IS group which has seized territory in Iraq and Syria, has reputedly called Saudi Arabia's Sunni rulers "apostate tyrants" and called on Saudis to rise against them.
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