City, the sole English club remaining in the competition, avoided incoming manager Pep Guardiola's Bayern Munich and holders Barcelona, who have knocked them out in the past two seasons.
Barca face Spanish rivals Atletico Madrid, Bayern meet Benfica, while Real Madrid take on Wolfsburg.
The quarter-finals will take place on 5-6 April and 12-13 April.
The Europa League draw - featuring Liverpool - takes place at 12:00 GMT.
Champions League quarter-final drawWolfsburg (Ger) v Real Madrid (Spa)Bayern Munich (Ger) v Benfica (Por)Barcelona (Spa) v Atletico Madrid (Spa)Paris St-Germain (Fra) v Manchester City (Eng)
Follow all the Champions League draw reaction here
Europe's nouveau riche go head-to-head
PSG, who have won the Ligue 1 title with two months to spare, will welcome City to the French capital in the first leg on Wednesday, 6 April.
The return leg at Etihad Stadium will take place on Tuesday, 12 April.
The teams have met only once before - agoalless draw in Manchester in the 2008-09 Uefa Cup.
Both clubs are barely recognisable from that meeting, when City were still in the infancy of Sheikh Mansour's ownership and PSG almost three years away from their Qatari takeover.
Laurent Blanc's side have gone on to dominate the French game, winning four successive league titles.
But, like City, the Parisians have not managed to conquer the Champions League, losing in the quarter-finals in each of the past three seasons.
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