The dawn raid in Palermo netted 80-year-old jeweller Settimo Mineo.
Mineo, who ran a family jewelry business, was allegedly behind an attempt to rebuild the "cupola" or ruling commission of Cosa Nostra in order to streamline its command structure and strengthen its position.
It was the first time clan leaders had gathered in such a forum for years, and followed the November 2017 death of Riina, prosecutors said.
Italy's chief anti-Mafia prosecutor, Cafiero De Raho, said the election of Mineo was significant because it showed that the centre of power of the Sicilian Mafia had shifted to Palermo from Corleone, its longtime base that was made famous by novelist Mario Puzo, who used the town's name for the main character in his 1969 novel The Godfather. The godfather is also known as the "capo dei capi" - or boss of bosses.
"With an extraordinary operation in the Palermo province, the police have dismantled Cosa Nostra's new "cupola"," wrote Interior Minister Matteo Salvini on Twitter.
Italian police arrest alleged head of Cosa Nostra and more than 40 other mafia mobsters
Following the operation, Deputy PM Di Maio hailed the arrests and vowed to stamp out organised crime.
In recent years police have hit the Cosa Nostra network hard.
Riina was notorious for his brutality.
Mineo was reportedly the head of the Pagliarelli district and considered the recently appointed kingpin of the entire organization. Italian media report that he avoided using a mobile phone and preferred to walk rather than travel by vehicle.
He is understood to have survived an assassination attempt in 1982, but two of his brothers were the victim of mob murders. Another brother, Antonino, was shot dead later. Italian daily La Repubblica says he told his interrogators: "I don't know who you're talking about, I fell from the clouds". Riina was arrested six months later.