Interior Ministry spokesman Maj Gen Mansour al-Turki identified the bomber today as 34-year-old Saad Saeed Saad al-Harthy.
The blast struck the mosque belonging to the Ismaili Shiite minority in the city of Najran after sunset yesterday, killing one person and wounding several others.
The SITE Intelligence Group, which monitors extremist activity online, says an IS affiliate known as "Hijaz Province" claimed it carried out the attack.
It was the fourth bombing targeting Saudi mosques and claimed by IS affiliates since May. The group considers Shiites as heretics and seeks to weaken the ruling Al-Saud family's legitimacy.