Citing a police spokesman, SPA said an eight-year-old child was taken to hospital for treatment for a gunshot wound in the incident in Awamiya town. It did not elaborate but identified the dead man 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.
Awamiya, in the oil-producing province's Qatif district, is the home town of prominent Shi'ite Muslim cleric Nimr al-Nimr, who was executed on Saturday, along with three other Shi'ites and 43 members of al Qaeda, on charges of terrorism.
Qatif has been the focal point of unrest among Saudi Arabia's Shi'ites since protests in early 2011 calling for an end to discrimination against the minority sect and for democratic reforms in the Sunni monarchy.
Residents of Qatif have staged angry protests since al-Nimr's execution, denouncing the ruling Al Saud dynasty, though the Sharqiyah activists said there was no demonstration taking place at the time of the shooting.