A civilian was killed and an 8-year-old child injured when gunmen opened fire on police in the hometown of executed Shiite cleric Nimr al-Nimr, Saudi police said on Monday.
The incident occurred as security forces were trying to recover a stolen heavy vehicle in Awwamiyeh, a police statement said.
Awwamiyeh and the neighbouring city of Qatif, strongholds of the Sunni kingdom's Shiite minority, have seen frequent protests and disturbances in recent years.
Al-Nimr, executed on Saturday, was sentenced to death in 2014 on charges of causing sectarian strife and disobeying the ruler.
The trial was condemned as unfair by human rights groups and the sheikh's supporters say he had only called for peaceful protest and criticized the ruling Al Saud family.
The execution has provoked a furious reaction from Shiite Muslims in the region. Saudi Arabia's regional rival, Shiite Iran, has said that the kingdom's rulers will suffer "divine revenge."
Saudi Arabia on Sunday broke off diplomatic relations with Iran after its embassy in Tehran was sacked by protesters.