The Gunners will host the first leg at the Emirates Stadium in a spectacle that will see England captain and former Tottenham striker Harry Kane return to London.
For City, it will be the third season in a row where they face Real in the knockout stage.
Should Arsenal and City win their respective ties, they will come up against each other in the semi-finals.
In the other quarter-finals, Paris Saint-Germain have been pitted against Barcelona with Atletico Madrid continuing their journey versus Borussia Dortmund.
Champions League draw in full:
Quarter-finals:
Atletico Madrid v Borussia Dortmund
Paris Saint-Germain v Barcelona
Semi-finals:
Atletico Madrid or Borussia Dortmund v Paris Saint-Germain or Barcelona
Arsenal or Bayern Munich v Real Madrid or Manchester City
When are the Champions League knockout ties?
The quarter-final first legs will take place on April 9th and 10th with the return legs on April 16th and 17th.
The semi-finals will start on April 30th and May 1st with the second legs on May 7th and 8th.
The Champions League final is on June 1st and will be played at Wembley Stadium in London.
