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.”
In recent years, there has been a spate of attacks on Ashura celebrations around the region by 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.