The police said the man, Leonardo Bertulazzi, 51, was head of logistics of the left-wing group, which carried out a series of attacks and political assassinations in Italy in the 1970s and 1980s.
The suspect was detained in the capital, Buenos Aires - a month after entering the country from Chile with false documents.
He now faces extradition to Italy, where Interpol has issued a warrant for his arrest.
Group's revival
Mr Betullazzi is accused of being part of an illegal association, illegal weapon possession, falsifying documents, kidnappings and terrorists acts, an Argentine police spokesman said.
He is the latest in a string of suspected Red Brigades members to be arrested in recent months.
Most of the original leaders of the Red Brigades were sentenced to long prison terms.
However, Italy's Justice Department has recently warned that the country could witness a revival of politically-motivated terrorism.
The statement followed a bomb attack near the Interior Ministry in Rome in February.
"The brigade saw a resurgence in Italy last year with attacks on councilmen," said Interpol spokesman Alexander Diniso.
In March, the group claimed the murder of Marco Biagi, an adviser to the labour minister, outside his home in Bologna.
During the 1970s and 1980s, Italy was plagued by domestic attacks from both right-wing and left-wing extremists, which killed hundreds and left a legacy of lingering political hostility.
Red Brigades's most notorious attack was the killing of former Prime Minister Aldo Moro in 1978.
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