The title was taken from a friend of Luis Buñuel, José Bergamín, who was writing a play with that title but never finished it. When Buñuel wanted to title his film, he asked for the rights of the title from his friend, but he answered that there was no trouble, because it was taken from the Bible, the Book of Revelation.
In his autobiography Luis Buñuel claims he was asked by Warner Brothers to work on a story that eventually was filmed as The Beast with Five Fingers (1946). "The Exterminating Angel" contains many of the elements of the earlier film including the large mansion, piano recital, and stabbing of a disembodied hand.
The film's cinematographer, Gabriel Figueroa, frantically approached director Luis Buñuel once he had seen the final cut of the film with concerns that there were several instances of repetition, something he was sure was an editorial mistake. Buñuel assured him that the repetition was a creative choice and reminded him that he edited his own films. The director recalled that Figueroa remained skeptical that the repetition was purposeful and not an editing mistake even after his explanation.
Luis Buñuel expressed frustration in regards to the film's low budget and the lack of amenities available on set in Mexico. As an example of these hardships, Buñuel recalled that the film operated on such an austere budget that he could not even afford to purchase fine table napkins for the dinner party scenes, nor could such napkins be easily obtained in Mexico at the time. He was only able to procure one such cloth napkin for a close-up shot of the dinner table when the film's makeup artist brought one from her home.
An early working title of the film was "The Castaways of Providence Street". Luis Buñuel took the title "El ángel exterminador" from his friend José Bergamín, the Spanish poet, who had mentioned it the year before for a play he wanted to write. Buñuel told Bergamin, "If I saw 'The Exterminating Angel' on a marquee, I'd go see it on the spot."