Madrid are aiming to become the first team in the Champions League era to win back-to-back titles and negotiated a tricky last-16 tie impressively, beating Napoli 3-1 home and away.
Bundesliga leaders Bayern remain in contention for a repeat of their 2013 treble and head coach Carlo Ancelotti will seek to deny Madrid, who he guided to La Decima – the club's 10th European title – in 2014.
Clasico rivals Barcelona face Serie A's dominant force in Juventus, having completed an historic comeback against Paris Saint-Germain – prevailing 6-5 on aggregate amid a breathless finale at Camp Nou to overturn a 4-0 first-leg defeat.
A typically imposing Spanish contingent is completed by Atletico Madrid, beaten finalists in 2014 and 2016, who eased past Bayer Leverkusen and will face Premier League champions Leicester City – conquerors of their La Liga counterparts Sevilla this week.
Monaco prevailed on away goals after a thrilling tie against Manchester City finished 6-6 overall and Leonardo Jardim's entertainers will travel to Borussia Dortmund for the first leg of the quarter-finals, which will be played on April 12 and 13 (AEDT).
Champions League quarter-final draw in full
Atletico Madrid v Leicester City
Borussia Dortmund v AS Monaco
Bayern Munich v Real Madrid
Juventus v Barcelona