The Reds were paired with the Spanish club during Friday morning’s draw for the last eight and the semi-finals in Nyon, Switzerland.
Jürgen Klopp’s side will be away from home for the first leg, before the return match takes place eight days later.
The winners of the clash will progress to a semi-final showdown with the winners of the tie between FC Porto and Chelsea.
The quarter-final games against Real are scheduled to be played on April 6 and April 14, both kicking off at 8pm BST.
Quarter-final draw
Manchester City v Borussia Dortmund
FC Porto v Chelsea
Bayern Munich v Paris Saint-Germain
Real Madrid v Liverpool
Semi-final draw
Bayern Munich or Paris Saint-Germain v Manchester City or Borussia Dortmund
Real Madrid or Liverpool v FC Porto or Chelsea