Both sides have already met on three occasions in 2012-13, and three more Clasicos are lined up over the next six weeks
The Santiago Bernabeu side had already booked their ticket for the final four earlier this week after proving too strong for Valencia.
The head-to-head record between the two sides stands at three victories apiece, with Madrid coming out victorious the last time they met in the semi-finals in 1992-93.
The Spanish cup has gone through four name changes throughout its history (Copa Alfonso XIII, Copa Presidente, Copa Generalisimo and Copa del Rey) and 31 Clasicos have taken place in the competition during this time. Barca won 15 of those games, six ended in a draw, while the Blancos bagged victory on 10 occasions.
The first leg of the semi-final will be held next week, while the return is scheduled for the last week of February.
Additionally, another Clasico takes place on March 2 as both arch-rivals meet in La Liga.
The Blaugrana and Madrid have already met on three occasions this season.