It called the shooting a “terrorist act” which killed the driver of a police car.
The attack happened at 1:45 am in the Saihat area of Qatif, a district on the Gulf coast, the ministry said.
It was the latest attack in Saihat, where gunmen in January shot dead two policemen escorting a truck used for transporting cash.
Last October, a shooter killed five people at a Shia meeting hall in Saihat.
Extremists from the militant Islamic State group claimed that attack as well as others against the minority community.
They have also said they murdered Saudi security personnel, but there was no immediate claim after Friday’s killing.
The shooting came despite the deployment of armoured vehicles at checkpoints in the area this week, according to a resident.
Tensions are high in neighbouring Bahrain, where there has been an escalating crackdown on the Shia majority, just over the causeway from Saudi Arabia’s Eastern Province.
Protests that began in Saudi Arabia’s east in February 2011 escalated after Saudi forces intervened weeks later in Bahrain to help crush a uprising there.
Hundreds were arrested in a Saudi crackdown after the initial protests, according to Amnesty International. Sporadic unrest has continued since.
Eastern Province is home to most of Saudi Arabia’s Shias, who have long complained of marginalisation in the Sunni-dominated kingdom.
In April, one policeman was lightly injured when a small bomb exploded outside a highway patrol station in the Eastern Province oasis region of Al-Ahsa, where much of the Gulf country’s oil reserves are located-DN
THE PASHTUN TIMES