Gunmen killed a civilian and wounded a child when they opened fire on Saudi police in the home village of an executed Shia cleric, state media reported on Monday.

Police came under "heavy fire" during the attack on Sunday night in the eastern village of Awamiya, the birthplace of the cleric who was executed on Saturday, said the Saudi Press Agency.

The shooting left a civilian dead and wounded an eight-year-old child, said SPA, without specifying if any police were among the casualties.

The dead man was identified as Ali Imran al-Dawood.

SPA said authorities were hunting what it called the perpetrators of a "terrorist" act. The security officers were seeking to recover stolen heavy equipment at the time of the shooting, SPA reported.

Activists operating under the Sharqiyah account on Twitter said a stray bullet hit the child inside his home after security forces opened fire on the street. The police then retreated to their checkpoint north of the city, they said.

Security forces were scouring the area for the assailants, the agency reported, citing a police spokesman in Eastern Province.

The kingdom's diplomatic missions in Iran came under attack following the execution.

The assaults on the diplomatic missions spurred Saudi Arabia to sever ties with Iran.

In recent years, the two countries have been divided over the war in Syria, where Iran is backing the regime, and the conflict in Yemen where a Saudi-led coalition is battling Shia rebels.