The two officers were escorting a truck used for transporting cash when they came under "heavy gunfire from unknown attackers in Sihat in Qatif province", a spokesman said.
The police spokesman, cited by the official SPA news agency, did not say whether the attack was being treated as political or criminal.
On January 4, police gunfire killed a civilian in Awamiya, the birthplace of Shiite cleric Nimr al-Nimr who had been executed two days earlier on "terrorism" charges.
The cleric, a virulent critic of the regime in predominantly Sunni Saudi Arabia, was revered in the east of the country.
His execution sparked protests in several Muslim countries and a crisis with Shiite Iran, Saudi Arabia's regional rival.
Riyadh cut diplomatic ties with Tehran, in a move followed by Bahrain and Sudan, while the United Arab Emirates and Kuwait recalled their ambassadors from Iran.