Two people were also wounded in the attack in the town of Dezful in Khuzestan province, the news agency said.
The southwestern province, which borders Iraq, has a significant ethnic Arab community, some of it Sunni, and has seen a number of armed attacks in recent years, according to Iranian media.
The assailants opened fire on the Shia place of worship from a car carrying no licence plates.
"It's not still clear whether the attack was a terrorist one," provincial police official Colonel Rahman Mousavi said.
"Investigators are reviewing the matter and will announce the results as soon as possible."
Ashura commemorations -- which climax on October 24 -- mark the killing of Imam Hussein, the grandson of the Prophet Mohammed, by the army of the Caliph Yazid in 680 AD. That event lies at the heart of Islam's divide into Shia and Sunni sects.
In recent years, there has been a spate of attacks on Ashura celebrations around the region by Sunni extremist groups which regard Shias as heretics.
On Friday evening, five people were killed in a shooting attack claimed by militants linked to the Islamic State group against Shia worshippers in Sunni-dominated Saudi Arabia, Iran's regional rival.
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