Security forces confronted both attackers as they headed toward the Imam Ridha mosque in the town of Mahasen, in eastern Saudi Arabia's al-Ahsa region in Eastern Province, where worshippers were holding Friday prayers, the press agency reported.
The bomber blew himself up as security personnel engaged him, and the other attacker exchanged fire with security forces, according to the Saudi Press Agency.
The gunman was arrested and was wearing a vest with explosives, the agency reported.
Pictures of the scene posted to social media showed several bodies on the ground.
This would be at least the fourth deadly attack on a Shiite mosque in Saudi Arabia
-- a kingdom where 85% to 90% of the citizens are Sunni -- since May. The previous three were claimed by ISIS
, the Sunni Islamist terror group, or one of its affiliates.
Saudi Interior Ministry spokesman Mansour Al-Turkey told CNN Arabic there was a "terrorism attempt" at the mosque in Mahasen.
"The situation has been handled," Al-Turkey said.
The identities of those who were killed or injured weren't immediately released. No immediate claim of responsibility for the attack was made.
Friday's assault comes after at least three Shiite mosques were attacked in the kingdom in 2015.
On May 22, a suicide bomber detonated himself, killing at least 21 people, at the Imam Ali mosque in the Persian Gulf-area village of Qudayh, in one of Saudi Arabia's few Shiite population centers in the majority Sunni kingdom.
A week later, a man disguised as a woman blew himself up -- killing at least three people -- outside a mosque in a predominantly Shiite neighborhood of Damman, the capital of Saudi Arabia's oil-rich Eastern Province.
ISIS claimed both May attacks.
In mid-October, an ISIS affiliate claimed an attack of its own -- a gunman opening fire on a Shiite mosque in the eastern Saudi Arabian city of Saihat. That attack killed at least five people, the Saudi Press Agency reported.