Justice Carmen Argibay was born in Buenos Aires, Argentina. She began her legal career in 1959 as a junior clerk in Correctional Court, then took the same position in 1961 in Juvenile Criminal Court, where she remained until 1965. She received her law degree from the Faculty of Law and Sciences at the University of Buenos Aires in 1964. Justice Argibay began work as a private attorney in 1965 but returned to the courts in 1969 and remained there until 1976, when she was removed following the military coup in Argentina. She was detained without charges for nine months.
On her release, Justice Argibay returned to private practice, but she returned to court work in 1984 when she was appointed trial judge. In 1988 she was promoted to court judge at the National Court of Criminal and Correctional Appeals, a position she held until 1993, when she became Judge to Criminal Oral Proceedings. In 2002, Justice Argibay was appointed ad litem judge to the International Criminal Tribune for the Former Yugoslavia (ICTY). In 2004 she became first woman nominated to the Supreme Court of Argentina.
Justice Argibay has also had a wide teaching career, including several teaching and advisory posts at the University of Buenos Aires. Since 1988, she has served on the Academic Advisory Board of the Higher Institute of Judicial Education for the postgraduate course in Administration of Justice. She has also been director of the Free Education for Women Workers and Retirees Programme of the Women's Library Association and a lecturer at the Universities of Belgrano and El Salvador.
Justice Argibay has also served as "Ambassador" to the Campaign for the Eradication of Violence by the Instituto Social y Politico de la Mujer and UNIFEM. In particular, she was one of the judges at the 2000 Tokyo Tribunal, which ruled on the responsibility of the Japanese armed forces for the sexual slavery imposed in the countries they invaded during the Second World War.
Justice Argibay was founder and first president of the Argentine Association of Women Judges and was the president of both the International Association of Women Judges and the Foundation of Women Judges.