President Cristina Fernandez de Kirchner said the Falklands were "Nato's military base" in the region.
British troops regained control of the archipelago after a 74-day war in which more than 900 people died.
Argentina claims sovereignty of the islands it calls Las Malvinas.
The new note is worth just under $7 (£4). On one side, it displays a map of the islands in the white and blue colours of the Argentine flag. Read more HERE