Probe leader Revd Tom O'Donnell said the four nuns will be investigated "to determine if there was a canonical crime and help the actions of the civil justice".
Former public works secretary Jose Lopez was arrested last month at the convent on the outskirts of Buenos Aires.
Police discovered wads of US dollars along with three other currencies.
Argentine media recently aired CCTV footage allegedly showing Mr Lopez bringing cash in through the convent's main entrance, aided by two nuns.
One of them is to appear before a judge on August 1.
