A group claiming links to Islamic State (IS) said it carried out the attack.
The interior ministry said a gunman opened fire at random before police intervened and shot the attacker dead.
Later, a group calling itself Islamic State-Bahrain State said that one of its "soldiers" had attacked "a Shia infidel temple" with an automatic weapon.
The group warned that "infidels will not be safe in the island of Mohammed".
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Correspondents say the name of the group appears to be a reference to the historic area of Bahrain, which once encompassed parts of what is now Saudi Arabia.
Other, smaller attacks against the Shia community in the east of Saudi Arabia were also reported on Friday evening.
The minority Shia community in the kingdom is increasingly being targeted. Most live in the oil-rich east, and many complain of discrimination.
In May, IS said it had carried out a deadly bomb attack outside a Shia mosque in the city of Damman.
A week before, more than 20 people were killed in the village of al-Qadeeh when an IS suicide bomber struck during Friday prayers at a Shia mosque.
That attack was the first to be claimed by a Saudi branch of IS.
Hardline Sunnis regard Shia Muslims as heretics.
Saudi Arabia, which is part of a US-led coalition against IS in Syria and Iraq, has previously been threatened by IS.
The Saudis are also leading a coalition of Arab states in an air campaign against Shia rebels in Yemen.
In the Ashura commemorations, Shias mourn the death of Hussein, a venerated grandson of the Prophet Muhammad.
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