The attack struck the Imam Reza Mosque in the neighborhood of Mehasin during prayers.
Images on social media showed wounded people laying on the mosque's floor.
The security officials said the three deaths were an initial toll. They spoke on condition of anonymity as a formal announcement had yet to be made.
An activist, citing witnesses, told Reuters earlier that an explosion was followed by gun attack on Imam Reza Mosque in the town of Mahasen in al-Ahsa region in the Eastern Province.
Residents said security forces were exchanging gunfire with five “terrorists”.
Mohammed al-Nimr told The Associated Press the attack struck the mosque during Friday prayers.
Al-Nimr, who is the brother of the executed cleric, Sheikh Nimr al-Nimr. said security forces and ambulances quickly surrounded the mosque.
He said that the attack was a shooting and that worshippers stopped the attacker from detonating a suicide bomb belt.
Saudi state media did not immediately report on the attack.
Shias in Saudi Arabia previously have been targeted in attacks by the Islamic State group in the kingdom.
Earlier this month, Saudi officials also executed a prominent Shia clericfrom the region, raising tensions in the area.
