The men were arrested in Brescia, a small city near Milan, police said in a statement, without naming either man.
It said the Tunisian man, 35, had created a Twitter account from which he posted "threatening messages signed ISIS" with the backdrop of famous landmarks such as Rome's Colosseum and Milan's cathedral.
Police were due to give details at a news conference later on Wednesday, Reuters reported.
Italian security forces have for months been on high alert against attacks at embassies, synagogues, churches, the Vatican and areas usually crowded with tourists.