"A man who opened fire at a hussainiya in Saihat was killed," Al-Ekhbariya news channel reported, without saying how he died.
A hussainiya is a Shia hall used for commemorations.
"Four wounded, including a woman, in the shooting," the channel said, adding that the attacker was 20 years old and his motives were unknown.
Read: Islamic State claims Yemen Shia mosque attack that killed 28
The shooting, in the Qatif area of Eastern Province, came two days after the start of commemorations of Ashura, one of the holiest occasions of the Shia faith.
During Ashura last year, gunmen killed seven Shia worshippers, including children, in the eastern town of Al-Dalwa.
The interior ministry said the suspects in the unprecedented attack were linked to the Islamic State group.
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