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 spokesperson said.
The police spokesperson, cited by the official SPA news agency, did not say whether the attack was being treated as political or criminal.
Two Saudi police shot dead in kingdom's east
On January 4, police gunfire killed a civilian in Awamiya, the birthplace of Shia cleric Nimr al-Nimr who had been executed two days earlier on "terrorism" charges.
Two days later, Shias protesting against Nimr's execution torched a bus in the same area.
The cleric, a virulent critic of the regime in predominantly Sunni Saudi Arabia, was revered in the east of the country.
Mass executions: Saudi Arabia executes 47 over terror charges
His execution sparked protests in several Muslim countries and a crisis with Shia 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.
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