Friday’s semi-final draw pitted defending champions Bayern against Carlo Ancelotti’s men, who scraped through 3-2 on aggregate against Borussia Dortmund.
Chelsea will play Atletico Madrid in the other semi-final, with the first legs taking place on April 22/23 and the return the following week.
Real’s pairing against Bayern brings together two clubs who have won the competition 14 times between them.
Five-time winners Bayern, quarter-final conquerors of Manchester United, are the defending champions. They beat fellow German side Borussia Dortmund at Wembley.
Real have won European club football’s top prize nine times – but not since 2002. Read more at Fox Soccer