To make matters worse for the current league leaders, they have the first leg of their Champions League tie away from home against Lyon on February 19, meaning that they will have to play seven games throughout February.
Barca overcame a 2-0 deficit from their quarter-final first leg against Sevilla, thrashing the Andalusians 6-1 in the return leg to progress 6-3 on aggregate.
The first leg will be on Wednesday in Barcelona, with the return match in Madrid on February 27, just before their Spanish league game at Santiago Bernabeu Stadium on March 3.More news: Samsung Galaxy S10 and Galaxy S10
Real Betis meanwhile were drawn against Valencia on the other side of the draw, giving the Andalusians a real opportunity of reaching the final which is being played at their own Benito Villamarín Stadium.
"If we are at our level we will go through", Barcelona director Guillermo Amor said. "We are talking about two teams with a lot of resources, with extraordinary players, and we always expect very tight games".
Madrid, who trail leaders Barcelona by 10 points in La Liga, have not won the Copa since the 2013-14 campaign.More news: Cuomo Shrugs Off Calls For Excommunication From Church Over Abortion Law
Arthur has played 15 league games (838 minutes) in LaLiga this season, and not one of the important fixtures has been lost. Four days after that, Madrid travels to the Netherlands to face Ajax in the last 16 of the Champions League.
The last time the two rivals met, Barca inflicted a humiliating 5-1 defeat on Real which led to the exit of manager Julen Lopetegui.
The Blaugrana are aiming for a record fifth consecutive Spanish League Cup title.More news: State of emergency declared in U.S. measles outbreak
"Real Madrid is the best team of the last century and therefore the best team in history".