The bounty by the Russian mercenary group, it said, was flagged to the minister by Italian intelligence services about 10 days ago.
It said Crosetto has not added to his security detail.
Earlier this week, Crosetto accused Wagner of driving migrants from Africa, especially Libya, in retaliation for Rome's support for Ukraine.
Wagner, which is best known at present for its role in Russia's invasion of Ukraine, is also active in Mali, Central African Republic, Sudan, Syria and Libya, where it backs strongman General Khalifa Haftar.
Wagner chief Yevgeny Prigozhin responded to Crosetto's claim that the Russian mercenary group was driving migration from several African countries to Italy by saying that the group did not deal with migrants.
Crosetto had accused the pro-Kremlin private Russian company and mercenary corps of waging a "hybrid war" and boosting emigration from the African countries where it is present.
Italian Foreign Minister Antonio Tajani responded to news of the bounty by calling it "unacceptable".
"We are between the ridiculous and the criminal," he said.
ANSA
