An eight month old baby, a two year old toddler and their mum, Valeria Carmona, 39, died in the accident after their vehicle collided into the back of a lorry around 350 miles from the capital Buenos Aires.
The children have been named as Jose and Antonio Bergoglio.
Their father, Horacio Bergoglio, 35, who is the son of the Pope's brother, is in a critical condition after the accident at midnight local time.
He's thought to have multiple injuries although this has not been confirmed.
Police are at the scene of the crash in the central province of Cordoba when the family was traveling on a motorway.
Vatican spokesman Fr Federico Lombardi said: "The pope was informed about the tragic accident. He is deeply pained."
He added the Pope wants "all who share in his grief to unite with him in prayer".
