State media reported two terrorists were involved in the shooting on Sunday.
One of the assailants was arrested. The other is said to be at large.
Three of those injured in the attack were in critical condition.
The terrorists attempted to enter the shrine through the Bab al-Mahdi Gate, and opened fire on the shrine servants.
The Shah Cheragh shrine in Shiraz was the scene of a similar attack by armed terrorists last year.
On October 26, 2022, an armed terrorist barged into the shrine, killing 15 pilgrims, including women and children, and injuring dozens more before he was shot and injured by security forces.
The terrorist later died of his wounds in hospital.
Several suspects were immediately arrested, and, some two weeks later, the Intelligence Ministry announced the arrest of 26 Takfiri terrorists for their involvement in the attack.