Leonardo Bertulazzi was given refugee status two years later but that was revoked when Argentina's right-wing president, Javier Milei, came to power.
"Bertulazzi is responsible for crimes that undermined democratic values and the lives of many victims," said a statement from the government in Buenos Aires.
The Red Brigades was a Marxist guerrilla group that kidnapped and killed a number of state officials in the 1970s and '80s, including a former prime minister, Aldo Moro. That period of political violence became known as "Years of Lead" because of the string of far-left and far-right crimes.
Bertulazzi had been part of the Red Brigades' Genoa section that kidnapped Pietro Costa on the street and then held him for 81 days before receiving a big ransom.
The money it received from the kidnapping was then used to buy a flat in Rome which was used in 1978 for the Red Brigades' most notorious crime, the kidnap and murder of Aldo Moro.
Moro was abducted when his car was ambushed on the way to the opening of parliament. He was held in the flat for 54 days before he was shot and his body abandoned in the boot of a Renault car in the centre of Rome.
Italian Prime Minister Giorgia Meloni praised the authorities in Buenos Aires for arresting Bertulazzi, adding that his detention was made possible by "intense and fruitful collaboration" involving authorities in both countries as well as by Interpol.
Bertulazzi's lawyers have appealed to Argentina's national commission for refugees (Conare) to prevent his extradition.
Italian attempts to have other former members of the Red Brigades extradited from France have failed in the courts.
