"Intelligence agents succeeded in identifying and arresting a terrorist group linked to Daesh, who intended to conduct terrorist attacks in central provinces and religious cities," a ministry statement said, using an alternative name for IS.
Ten of the suspects were arrested outside Iran "through intelligence-sharing with one of the intelligence services in the region," the statement said, without naming the country or giving further details.
Weapons and ammunition were recovered during the arrests, and the suspects were reportedly trying to smuggle them into Iran inside home appliances.
Tehran suffered a rare and deadly twin attack on June 7, claimed by IS, when gunmen and suicide bombers attacked the parliament complex and the mausoleum of revolutionary founder Ayatollah Ruhollah Khomeini, killing 17 people.
Iranian security officials have since arrested dozens of suspects linked to the attack, and claim to have killed its chief planner.
On June 19, Iran also fired missiles into northeastern Syria in retaliation, targeting an IS command base in Deir Ezzor province.