The jihadist group claimed responsibility for Wednesday's attacks that killed 17 people.
The intelligence ministry said 41 suspects were arrested in Tehran, in the northwestern provinces of Kermanshah and Kurdistan, and in West Azerbaijan, near the borders with Iraq and Turkey.
It described the suspects as "agents of Daesh", an Arabic acronym for the Islamic State group, and said they included "operational teams".
Documents and equipment "for carrying out terrorist operations" were also seized, the ministry said in a statement.
The attacks on Tehran's parliament complex and the shrine of revolutionary leader Ayatollah Ruhollah Khomeini also wounded more than 50 people and were the first claimed by IS in Iran.
Iran has said five Iranians, who had joined IS and travelled to its Iraq and Syria bastions, carried out the attack.
It also announced just after the attack the arrest of five suspects at the parliament complex and the Khomeini shrine, in addition to the arrests announced on Friday.
Intelligence Minister Mahmoud Alavi has said Iran identified several jihadists, where they meet and where they hide.
Security forces have found explosive vests and other equipment, as well as an abandoned car, packed with at least 22 pistols, in Kermanshah province.
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