The pre-dawn attack happened near a farm in the Saihat area of Qatif, on the Gulf coast.
A ministry spokesman said the suspect or suspects had not immediately been identified.
It is the latest incident in the area as police continue to hunt suspects on a list of 23 wanted people issued in 2011 after Shiites in Eastern Province began protests.
Shiites in the Sunni-dominated kingdom have complained of marginalisation.
Last week, two Indian passersby and a policeman were wounded when officers came under fire from a farming area in Qatif.
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In early October gunfire erupted in the Shiite town of Awamiya, near the Gulf coast city of Dammam, after police sealed it off with armoured vehicles.
Police seized a large amount of ammunition during a search of a farming area there, the interior ministry said.
Last month, Saudi Arabia's Supreme Court confirmed a death sentence against Shiite cleric Nimr al-Nimr, a leader of anti-government protests convicted of sedition and other crimes.
Activists are calling for the sentence not to be carried out, saying Nimr engaged only in peaceful opposition.
Over the past year, Saudi Shiites have been targeted by suicide bombings and shootings claimed by Sunni extremists of the Islamic State group, who consider them heretics.
In the latest attack, a gunman killed five Shiites in Saihat last month during commemorations of Ashura, one of the holiest observances of their faith.