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.
The police officer is at least the third person killed in the Gulf coast town of Awamiya since Wednesday.
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.
- A wasteland -
Images purportedly from the area and circulating on social media Tuesday showed a wasteland of buildings apparently pockmarked heavily by gunfire and with some showing signs of burning.
Rubble and damaged cars lay in the narrow streets.
Residents first reported gunfire on Wednesday in Awamiya, as authorities moved on the Almosara district.
On Saturday residents told AFP that people from the Almosara area had been asked to leave, and some sought shelter with people in adjacent districts.
In March the ministry said a teenage suspect died from wounds after Saudi police "responded" under fire while looking for suspects hiding among abandoned homes in Almosara.
A resident at that time told AFP people had been living for more than a month in Almosara resisting the urban renewal project.
They had no water and their electricity came only from generators, the resident said, adding they wanted to be given new houses and the area kept as a historical district.
Awamiya was the home of Nimr al-Nimr, a Shiite cleric put to death in January last year for "terrorism".
Nimr was a driving force behind protests by Shiites that began in 2011 and developed into a call for equality in the Sunni-majority kingdom.
But residents in the Awamiya area have also complained about the presence of people involved in criminal activity including the drug trade.
Shiites in eastern Saudi Arabia live just across from Shiite majority Bahrain where authorities have accused Iran of trying to spark unrest.
Riyadh's Sunni rulers regularly accuses Shiite-dominated Iran of interference throughout the Middle East.
Iran is expected to be a focus this weekend when US President Donald Trump, on his first overseas trip, holds summits in Riyadh with Muslim leaders from the Gulf and around the world.