Carafa was born in Andria in the Kingdom of Naples (modern day Italy), of the family of the Counts of Montorio, and a relative of Pope Paul IV.

In 1648 Carafa called the forty-year old letterato Daniello Bartoli from his itinerant activities as a preacher around Italy to the Casa Professa (Rome) and a permanent position there as the official historian of the Jesuit order.

A great scandal occurred in Spain because of unsuccessful business speculations by a coadjutor brother, and in France on account of the open apostasy to Calvinism of a priest; but the martyrdom of Isaac Jogues, Brébeuf, Neville, and others in Canada and England showed that the Society's ancient fervour had not relaxed.

According to St Louis de Montfort in True Devotion to Mary, Carafa would wear an iron band around his feet as a mark of his servitude to Jesus.

Besides personal correspondence his only known writing as Superior General was his letter addressed to all Jesuits: De mediis conservandi primævum spiritum Societatis (The means of preserving the primitive spirit of the Society).