That prompted a withering putdown from Italian Prime Minister Matteo Renzi who tweeted: "In this country the judges follow the law and the Italian constitution, not the Turkish president. That's called 'the rule of law'."
Erdogan's eldest son Bilal, who was studying in Bologna, has been under investigation since February by judges who suspect him of involvement in money laundering.
An exiled Turkish businessman opposed to the Erdogan government has accused Bilal of having arrived in Italy with large stashes of cash and a heavily-armed bodyguard unit that had travelled on diplomatic passports.
"My son is meant to return to Bologna to finish his doctorate but is in danger of being arrested," Erdogan said in an interview with Italian news channel Rai News24.
"In this city they call me a dictator and demonstrate for the PKK (Kurdish militants). Why does no one intervene?
"Is that the rule of law? This affair could compromise our relations with Italy."
Erdogan added: "Let Italy's judges deal with the mafia, not my son."
The spat with Italy came as Erdogan launched a bitter attack on all of Turkey's Western allies over his reaction to a July 15th attempt to overthrow him, which has led to a crackdown that has raised fears for the survival of democracy in the country.