She has previously praised the pontiff for his role in rebuilding relations between the United States and Cuba.
President de Kirchner has caused controversy by previously stating she wants to reclaim the Falkland Islands.
Reuters reported that the meeting lasted just under two hours and the pair exchanged gifts.
On Monday during her visit to Rome, President de Kirchner will also be attending the 39th Conference of the United Nations Food and Agriculture Organization and will be meeting the Italian president, Sergio Mattarella.
The Pope is expected to travel to a number of countries this year visiting world leaders, including the United States and Cuba in autumn.