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 told reporters about 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."
Juve director Pavel Nedved said: "Bayern are one of the hardest teams that we could have faced. We have to approach the tie positively. I'm proud that Juve are among the top eight sides in Europe and the only Italian side in the draw."
Barcelona, who overhauled a 2-0 first leg deficit to beat AC Milan in the last 16 this week, will face rising force PSG with the first leg in France.
PSG's former Barca frontman Zlatan Ibrahimovic is set to miss the first leg through suspension.
Leonardo, sports director at the Qatari-backed Ligue 1 leaders, told TV channel BeIN Sport: "We are going to play against the best team - not just because of what they did this week, 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."
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.
Real director Emilio Butragueno told Sky Sports: "We need to get a very good result at home because we know that their fans will make it very difficult there.
"Galatasaray have overcome some tough hurdles and they will be very competitive and by signing Didier Drogba they have improved tremendously."
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.
Draw for the Champions League quarter-finals:
Malaga v Borussia Dortmund
Real Madrid v Galatasaray
Paris Saint-Germain v Barcelona
Bayern Munich v Juventus
First legs to be played on April 2 or 3, second legs April 9 or 10.
