The defending champions, who were routed 4-0 by their local rivals last month, were drawn Friday to face Atletico in a rematch of last year's final.
Also, 2013 champion Bayern Munich will face FC Porto, Paris Saint-Germain and Barcelona will meet again after playing in the group stage this season, and the final match-up pits Juventus against Monaco.
Madrid won its record 10th title in the continental competition last year with a 4-1 victory over Atletico, which has dominated their most recent match-ups.
Atletico and Real Madrid will be facing each other for the seventh and eighth times this season, with Real Madrid yet to register a win. Last month, Madrid was handed its biggest defeat in four years as it slumped to a 4-0 loss at Atletico in the Spanish capital derby.
The first leg will be played at Atletico's ground on April 14, with the return game on April 22.
"They're (Atletico) a side who know how to compete, they let in few goals, are good from dead balls and get the best out of each situation," said former Real Madrid player Emilio Butragueno, now a director of institutional relations at the club. "You never know if it's an advantage playing the second leg at home. We have to be at our best because we know exactly the difficulties that we're going to face."
This year's final will take place at the Olympic Stadium in Berlin on June 6.
PSG will be without its main striker against Barcelona for the first leg at the Parc des Princes after Zlatan Ibrahimovic was suspended for one game following his sending off against Chelsea in the previous round.
PSG beat Barcelona 3-2 at home in the group stage but lost 3-1 at the Camp Nou. The teams also met in the quarterfinals two seasons ago, with Barcelona progressing on away goals.
After reaching the quarterfinals for the 14th time, Bayern will be favoured against an unexperienced Porto side, which beat the German giants in the 1987 European Cup final.
"The draw is the draw. All teams have a special quality," Bayern coach Pep Guardiola said. "Porto have a great team and a beautiful stadium. They are very strong physically and attack with a lot of pace. In the quarterfinals you can't expect an easy match."
Porto won the 2004 trophy under coach Jose Mourinho by defeating Monaco in the final.
"The atmosphere in Porto is very heated," Bayern goalkeeper Manuel Neuer said. "With these fans it won't be easy for us, but we have played in many different stadiums with varying atmospheres and we will know what to expect."
Juventus, which made it to the quarterfinals for the second time in three seasons, wanted to avoid Bayern. Its hopes were fulfilled with a relatively easy draw.
"Juventus are among the biggest sides," said Monaco coach Leonardo Jardim, whose side survived an Arsenal onslaught to progress on away goals. "They are the favourites. We're lucky to have the second leg at home. We'll try to make the most of this quarterfinal."
Juventus will, however, be diminished against the Principality side, missing France midfielder Paul Pogba until early May after he picked up a thigh injury in the second leg of the 5-1 aggregate win over Borussia Dortmund.