Anti-terrorism police arrested the man, identified in the media as 58-year-old Abdel Rahman, an Egyptian with Italian citizenship, in the city of Foggia in Puglia.
His bank accounts were seized and the centre he ran, Al Dawa, was searched and sealed off.
Accused of apology for terrorism and association for the purpose of terrorism, Rahman is said to have praised Isis attacks on social media and shared material glorifying the terrorist group.
He is suspected of attempting to spread similar propaganda at the cultural association of which he was president, and where he was in charge of teaching religious lessons to children as young as 4 years old, according to La Repubblica.
Secret recordings caught him telling youngsters to attack "unbelievers" with swords and bombs, the newspaper said.
The newspaper said Rahman was arrested as part of an investigation codenamed "Bad Teacher", the latest in a series of anti-terror operations in Foggia within the past year.
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There have been four arrests and two expulsions since May 2017, according to Rai News, all of which are thought to have had some connection to the Al Dawa centre.
In July, police arrested a Chechen man who frequented the centre and was believed to belong to a terrorist group in the Caucasus. Having participated in violence in Chechnya and Syria, he was allegedly attempting to recruit others to carry out extremist attacks.
Separately, a Tunisian and an Algerian national were arrested and two Albanian brothers expelled on charges of aiding or promoting violent groups.
Italy has taken a hardline approach to so-called apologists for terrorism.
In early 2015 the country's cabinet approved a slew of anti-terrorism measures, including jail terms of up to six years for "foreign fighters" as well as those who recruit would-be jihadists. The measures also included confiscating the passports of suspected militants and giving more powers to Italy's intelligence services.
Since then, the country has deported well over 100 people for religious extremism.