A member of the special police emergency forces died when "a rocket-propelled grenade (was) launched from inside the neighbourhood" and hit his patrol unit in the Almosara area of Awamiya, the ministry said in a statement.
"Five others were injured and taken to hospital," it said.
Awamiya is a town of 30,000 in Qatif district of Eastern Province, where most of the Sunni-ruled kingdom's Shiites live.
The town, in a region where Shiites have long complained of marginalisation, has been the scene of repeated security incidents.
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The unrest centres on Awamiya's old Almosara district, which is the site of a redevelopment project.
"It's really war," said an area resident who reported his home has been shaken by explosions in the past two days.
On Friday the ministry said a two-year-old boy and a Pakistani died when gunmen from within Almosara opened fire on passersby, security officers and workers on the project.
Residents gave a higher toll.
Criminals engaged in the drug and arms trade tried "to jeopardise the project and protect their terrorist activities that they launch from the abandoned houses in the neighbourhood", the ministry said at the time.