FC Barcelona will play against PSG with the first leg in France.
Paris St Germain sports director Leonardo told TV channel BeIN Sport: “We are going to play against the best team not just because of what they did this week (coming back to beat AC Milan), but because of what they have been doing in the past years.
“It is not easy but no draw would have been easy anyway. Paris deserves to be part of the big party.”
Bayern, beaten finalists last season when Chelsea lifted the trophy, will first host the Serie A champions who are back in the quarter-finals after a seven-year absence.
“That is certainly not a dream draw for us,” Bayern chief executive Karl-Heinz Rummenigge said of meeting the twice European champions.
“Statistically we have not had good experiences with Juventus. It will be difficult and we will need to have two good days against them to reach the semis.”
Nine-times winners Real Madrid will take on Galatasaray in a tie which pits Jose Mourinho, coach of the Spanish side, against his former Chelsea player Didier Drogba. Real are at home first.
Bundesliga champions Borussia Dortmund were drawn against Champions League newcomers Malaga in the other quarter-final with the Spaniards at home in the first leg.
“We can live with this draw,” Dortmund sports director Michael Zorc said. “At least it is better than playing Barcelona, Real or Bayern.”
The first legs will be played on April 2 or 3 and the second legs on April 9 or 10.
England do not have a team in the Champions League quarter-finals for the first time since the 1995-96 season.