Segunda B's Ponferradina are from the town of Ponferrada in north-west Spain, whose population of around 70,000 would fit inside the Santiago Bernabeu stadium, the home of the world's richest club by income.
"It's the best thing that could have happened to us," Ponferradina coach Claudio Barragan told reporters. "With society going through such difficult times it's a lift for the people.
"For the modest teams the presence of an entity such as Real Madrid is also an economic boost."
Jose Mourinho's side beat Barcelona 1-0 after extra-time in last year's final.
Champions League competitors Valencia and Villarreal were drawn against third-tier Cadiz and Mirandes respectively.
There were four all-La Liga clashes: Real Mallorca playing Sporting Gijon, Racing Santander hosting Rayo Vallecano, Getafe against Malaga and Real Sociedad versus Granada.
The first legs are to be played on December 13 with the returns on December 21.
Barca's first leg at nearby Hospitalet will be played on November 9, as the team are playing in the World Club Cup in Japan in December, while Athletic Bilbao and Atletico Madrid will have their first legs moved to December 8 because of Europa League fixtures.
