The draw took place in La Cartuja, the Olympic stadium in Seville that will host the final next April, and is organised so that all LaLiga clubs avoid each other and are instead drawn with teams from the lower reaches of the Spanish football pyramid.
Atletico are the only one of the traditional 'big three' involved and face a trip to Tercera Division side Cardassar, who are from a small town on the island of Mallorca.
Sevilla, Spain's fourth Champions League representative this term, will stay in Andalusia when they go to Ciudad de Lucena and Valencia have been drawn against Catalonian team Terrassa.
Ties will take place on December 16 between the 112 clubs involved at this stage.
Madrid, Barca and 2019-20 Copa finalists Real Sociedad and Athletic Bilbao have byes to the third round due to their participation in the expanded Supercopa.
Athletic and La Real were unable to play their historic all-Basque final earlier this year as planned due to the coronavirus pandemic, with the match postponed indefinitely at the time.
Recent media reports suggest the match is due to be rearranged for April 4, 2021, two weeks prior to the 2020-21 final.