The incident took place at around 5.45 p.m. local time (1415GMT) when three heavily-armed men attacked the Shah Cheragh shrine in the historic city of Shiraz in the Fars province.
According to local reports, two attackers were immediately apprehended by local security guards and search is underway for the third attacker who apparently managed to flee from the scene.
Although details are still unclear, reports said a woman and two children were among the victims.
Shah Cheragh shrine, which houses the grave of a revered Shia scholar, is a popular pilgrim destination in southern Iran, thronged by both local and foreign pilgrims.
It came amid widespread protests across Iran over the death of a young Iranian woman, Mahsa Amini, in police custody last month.
Wednesday marked 40 days since her death and saw fresh protests in several cities, including Tehran, amid heavy deployment of police on the streets.
There were also reports of clashes between police and protesters in her native town of Sanandaj in western Iran during a ceremony to mark the 40th day since her death.
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