Madrid will host the first leg on April 9 or 10 and the return will be the following week in Manchester.
The teams met in the semi-final in the last two seasons, with City hammering Real 4-0 at the Etihad Stadium last season on their way to winning their first Champions League title.
Kylian Mbappe's path to a first Champions League title with Paris Saint-Germain in his farewell season there is a difficult one, as the French champions face Barcelona.
Arsenal have been drawn against Bayern Munich, whose star striker Harry Kane will go back to north London after leaving the Gunners' arch-rivals Tottenham last off-season.
Atletico Madrid meet Borussia Dortmund in the other game.
UEFA also made the draw for the semi-finals, which ensured Mbappe and PSG cannot meet Real Madrid - the team he is expected to join in the summer - until the final.
That draw arguably put the four strongest teams in the same half.
The winners between Real Madrid and Man City will be away in the first leg against Arsenal or Bayern.
Atletico or Dortmund will host the first leg against PSG or Barcelona.
There was a familiar and powerful look to the draw. It featured five European champions - who have combined to win 27 of the previous 68 titles - and three beaten finalists in Arsenal, Atletico and PSG.
The semi-finals will be played between April 30 and May 8. The final is on June 1 at Wembley Stadium in London.
In the Europa League, Liverpool have been drawn against Italian side Atalanta in the last eight, while West Ham face a tough challenge against Bundesliga leaders Bayer Leverkusen, who are unbeaten in 37 matches in all competitions this season under their highly-rated coach Xabi Alonso.
Liverpool and West Ham cannot meet until the final in Dublin after the semi-final draw also kept the Premier League teams apart.
If Liverpool progress, they'll meet either Olympique Marseille or Sporting Lisbon in the semis, while West Ham or Leverkusen will play the winners of an all-Italian tie between AC Milan and last year's runners-up Roma.
Aston Villa will go up against French side Lille in the Europa Conference League quarter-finals.
