Mukhtar Ablyazov's daughter Madina accuses the diplomats in the lawsuit, including Adrian Yelemessov, Kazakhstan's ambassador to Italy, of "aggravated kidnapping" over the incident.
Ablyazov's wife Alma and daughter Alua were detained in Rome on May 31st and flown to Kazakhstan in a specially-chartered jet on what the lawsuit says were spurious charges of having false papers.
The lawsuit also asks prosecutors to identify Italian officials who were responsible for assisting in the hastily-arranged extradition.
"We are convinced that abuses and grave omissions were committed and we believe prosecutors will be able to clarify," Madina Ablyazova's lawyer, Astolfo Di Amato, told reporters in Rome.
Mukhtar Ablyazov, a powerful former energy minister and critic of Kazakhstan's regime, is currently in detention in France awaiting possible extradition to Ukraine for embezzling billions of euros.
Russia and Kazakhstan also want his extradition.
Once close to Kazakhstan's elite, Ablyazov fell out of favour and became a foe of strongman Nursultan Nazarbayev, who has ruled the oil-rich former Soviet republic for almost 22 years.
Ablyazov was jailed in 2002 for abuse of power and illegal business activities after co-founding an opposition party, in a move widely seen as a bid to silence him.
He was quickly pardoned and released, however.
Returning to finance, where he had made his fortune, he led the Kazakh BTA Bank, which also had interests in Ukraine.
But in 2009, he fled to Britain amid accusations he stole billions of dollars in state and investor funds.
He is believed to have stayed there until he was sentenced to 22 months in jail for contempt of court.
He did not surrender to the British authorities and is then thought to have moved to Italy before his arrest in the south of France.