Officers "came under fire from an unknown gunman firing from the farms" near Awamiya killing one soldier, the Saudi Press Agency said.
A manhunt was underway, it added.
Awamiya, just west of Dammam city on the Gulf coast, has witnessed clashes between security forces and protesters from the minority Shiite community.
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In February, a firefight in Awamiya left two policemen and two suspects dead. Other shootings have occurred there in subsequent months.
Most of Saudi Arabia's Shiite minority live in the oil-rich east, and many complain of marginalisation.
Since 2011, protests and sporadic attacks on security forces have occurred in Shiite areas, leaving around 20 Shiite youth dead.
Activists say several death sentences have also been handed down by courts in the kingdom since the demonstrations began.