The ministry said members of an "anti-Islamic terrorist takfiri group" had been arrested and explosives seized.
The intelligence ministry gave no further details about the suspects.
"Takfiri" is a term used by officials in Shia Iran to describe Sunni extremists who declare other Muslims as apostates deserving of death.
Iran is currently helping both the Syrian and Iraqi governments battle the jihadist group, Islamic State (IS), which considers Shia to be infidels for their veneration of the Prophet Muhammad's family and other beliefs and practices.
Militants claiming to be defending the Sunni minority community in south-eastern Iran have also carried out a number of attacks against the state in recent years.
The intelligence ministry said the investigation by its agents - whom it described as "Unnamed Soldiers of the Lord of Ages" - was continuing "inside and outside" Iran.
"Updated information will be released to the great Iranian nation as soon as the proper conditions are established," it added.
The Fars news agency cited the secretary of Iran's Supreme National Security Council, Ali Shamkhani, as saying the bomb attacks had been planned for the Islamic holy month of Ramadan.
Last month, Intelligence Minister Mahmoud Alavi said 20 terrorist groups that had planned to carry out bomb attacks and cause insecurity had been dismantled.