Qatif, an eastern province in Sunni-ruled Saudi Arabia, has been hit by a string of attacks over the past week, some of them deadly.
Police said an off-duty officer was wounded late Sunday when gunmen opened fire on his car as he was driving by private farmland.
And two civilians were admitted with gunshot wounds early Monday to a hospital in Qatif's town of Awamiya, police added.
All three are in stable condition.
Violence over the past week has gripped Qatif, where two policemen were killed in two separate bombings targeting their patrols on Tuesday and Thursday.
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Last month, three people, including an officer, were also killed in bombings in the area.
Saudi authorities have said they are treating the bombings last week as "terrorist crimes" and have blamed drug and arms traffickers for unrest in the area.
Residents have accused police of opening fire on civilians and give a higher death toll.