"The last suspect in the Shiraz terror case has been detained," the minister was quoted as saying by Tasnim news agency.
This brings up to five the number of arrests made in the wake of Sunday's gun attack at the Shah Cheragh mausoleum in the southern city of Shiraz that left one person dead and eight others injured.
No group has claimed responsibility for the shooting, but Iran was frequently targeted in the past by Sunni militants from the Islamic State, a terrorist organization (banned in Russia).