La Real will take on second division Mirandés in the last four while Athletic Club - who have won the competition on 23 occasions - will take on Granada.
It follows a week of shocks in the quarter-final stage of the competition as Real Sociedad - who have won the competition twice but not since 1987 - secured a stunning 4-3 victory at Real Madrid while Athletic Club eliminated Barcelona.
Mirandés are the story of the competition to date - sitting 11th in Spain’s second tier, they have defeated full-strength sides from Celta de Vigo, Sevilla and Villarreal en route to the last four.
Granada also caused an upset as they eliminated competition holders Valencia earlier this week - the Andalusian club reached the final just once, in 1959.
The first legs of the semi-final will take place on 12 February with the return fixtures being held on 4 March.