"A person who opened fire on a husseiniya was killed, and the attacker was in his twenties," reported government-run channel, Al Ekhbariya TV.
A resident reached by telephone told Reuters that the assailant approached the meeting hall in the eastern city of Saihat in a taxi but was stopped at a checkpoint manned by volunteers protecting the site.
Police arrived and a gunbattle broke out, which the resident said injured several people and left the shooter dead.
Islamic State, an ultra-violent Sunni group based in Iraq and Syria, claimed responsibility for the attack in a statement posted online.
"With the approval of God Almighty, the soldier of the caliphate Shuja al-Dawsari, may God accept him, set his Kalashnikov upon one of the apostate polytheists` temples."
Amateur video described as filmed by activists inside the hall showed worshippers, including young children, crowding towards the entrance at the sound of gunfire before retreating in fear.
Islamic State has launched a series of deadly attacks inside the kingdom in recent months, aiming to stir sectarian confrontation on the Arabian peninsula and bring about the overthrow of Gulf states` ruling dynasties.
A suicide bomber killed at least 15 people in an attack on a mosque used by members of a local security force in southwest Saudi Arabia in August and two separate suicide bombings on Shi`ite mosques in May killed 25 worshippers.
Groups of volunteer security guards have been formed around Shi`ite holy sites of the kingdom, whose rulers follow a strict version of Sunni Islam shared by the majority of the country`s population.
Some local activists have accused security forces of not doing enough to thwart the assaults, a charge officials deny.
Saudi authorities said in July they had rounded up 431 Islamic State suspects and had foiled plots to attack places of worship and security forces.
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