The probe leader Reverend Tom O'Donnell, said they would try "to determine if there was a canonical crime".
Last month, a former government minister was arrested outside their convent near Buenos Aires.
He was allegedly trying to hide almost $9m (Â£6.8m) in cash and jewels.
Nuns working at the Our Lady of the Rosary of Fatima religious community about 55km (35 miles) west of the capital Buenos Aires called the police after they saw a man throwing plastic bags full of money over a wall.
He was allegedly Jose Lopez, who was the public works minister in the former government of Cristina Fernandez de Kirchner.
The media in Argentina recently showed CCTV footage allegedly showing Mr Lopez bringing the bags with wads of cash in several currencies and jewels into the convent, helped by two nuns.
A total of four nuns are said to have helped him. One of them is due to appear next month before a judge.
Since Argentina's new President, Mauricio Macri took over earlier this year, there have been a series of investigations of former officials for money-laundering.
The Roman Catholic Church in Argentina has launched an investigation into whether four nuns helped to hide a hoard of cash and jewels.