The pontiff said he was given it to supplement his mother's milk after being given a gift of two donkeys by an Italian company, Eurolactis Italia.
Founder Pierluigi Christophe Orunesu said: "The Pope, who named himself after St Francis, the protector of all animals, revealed that he himself, when he was a baby, was brought up on donkey's milk."
Donkey's milk is more similar to breast milk than that from a cow.
It's thought the two animals, named Noè and Thea, will be kept at the Pope's Summer residence, Castel Gandolfo.
It has a small farm producing fruit, vegetables and honey for the Vatican.