Chief Justice of the Fars Province Kazem Mousavi said on Monday four suspects linked to the incident were arrested after investigations.
The main assailant opened fire at the pilgrims with an AK-47 rifle and made an attempt to enter a more crowded area of the shrine before being arrested.
Officials put the number of the wounded at eight, three of them in critical condition.
The Daesh terrorist group has claimed responsibility for the assault.
This is not the first time armed terrorists have targeted the Shah Cheragh shrine.
Last year, an armed assailant opened fire on people inside the shrine, killing 13 pilgrims, including women and children, and injuring dozens more before he was shot and injured by security forces.
The terrorist, a foreign national, later died of his injuries in the hospital.
