Officials in predominantly Shi'ite Iran have said in recent weeks that Sunni militants from Islamic State have been trying to target the country.
Alavi said the arrests took place in the last week in Tehran and three other provinces in central Iran and along the border.
The minister told a news conference in Tehran that the group had planned to attack busy public locations with remotely detonated explosions, suicide attacks and car bombs, according to Fars News.
One hundred kilograms of explosive material has been confiscated and an additional two tons of explosive material was intercepted before reaching the suspects, who are currently being interrogated.
Details of the attack come one day after the Ministry of Intelligence issued a statement saying it had thwarted a major terrorist attack.
Members of Iran's Revolutionary Guard have fought against Islamic State militants in Iraq in a bid to support the Shia-led government in Baghdad. Guard members and volunteers are also fighting against Sunni militants in Syria to support President Bashar al-Assad.
Iranian security forces announced last month that they had arrested a dozen Islamic State fighters in the east and west of the country, and also more than 50 sympathisers who were promoting the group's ideology on the Internet.
Iranian intelligence minister Mahmoud Alavi said the arrests took place in the last week in Tehran and three other provinces in central Iran and along the border.
Iran has arrested 10 Sunni Muslim militants who were planning to bomb 50 targets across the country, Iranian intelligence minister Mahmoud Alavi said on Tuesday, according to the Fars News site.
