The Catalans, who are searching for their third European victory in five years, avoided an El Clasico against Real Madrid, who will go up against Galatasaray in the final eight.
The Ligue 1 outfit will host Barca for the first leg on April 2 or 3, while last year's La Liga runner-ups will take on PSG in the return leg on April 9 or 10.
PSG striker Zlatan Ibrahimovic will be unavailable for the home fixture due to a UEFA suspension.
Champions League quarter-final matches:
Malaga vs. Borussia Dortmund
Real Madrid vs. Galatasaray
Paris Saint-Germain vs. Barcelona
Bayern Munich vs. Juventus