Giuseppe Salvatore Riina was among some 20 people taken into custody, including several prominent businessmen from the Sicilian capital Palermo.
Police say the 25-year-old was involved in establishing Mafia-controlled companies to launder money from protection rackets, drug-trafficking and tenders for public building contracts on the island.
Giuseppe is one of four Riina children, and the second to be arrested for following in his father's footsteps.
Closing in
Salvatore, now 70, was the Sicilian Mafia's "Boss of Bosses" who led the organisation through one of its most bloody and ruthless periods. He was arrested in 1993.
He is serving a string of life sentences for numerous crimes, including ordering the 1992 car bomb killings of anti-Mafia judges Giovanni Falcone and Paolo Borsellino. Mr Falcone's wife was also killed in the blast, as were the bodyguards of both magistrates.
Giuseppe's older brother, Giovanni, was sentenced by a court in Palermo to life in prison for four murders. He had been in police custody since 1997.
Police have been gradually closing in on the Sicilian Mafia. Earlier this year, more than 30 suspected members of a gang linked to Mafia leader Bernardo Provenzano were arrested.
It is thought Mr Provenzano took over the reins of the clan after Salvatore Riina's arrest. He has been a fugitive for nearly 40 years, and has received multiple life sentences from Italian courts in his absence.
Police have just one photograph of him, taken in 1959. It features a clean-cut man in his 20s who would bear little resemblance to a man who is now 70.