Champions League debutants Malaga, who have overcome pre-season financial turmoil to reach the last eight, take on German champions Borussia Dortmund while Real Madrid will face Galatasaray.
Nine-times winners Real's tie pits their coach Jose Mourinho against his former Chelsea player Didier Drogba and brings back memories of an epic clash between the two sides 12 years ago.
For the first time since the 1995-96 season, the last eight line-up was devoid of English Premier League teams after Manchester United and Arsenal went out in the last 16 and Chelsea and Manchester City failed to progress beyond the group stage.
Although there was no seeding, the draw failed to produce any dream clashes such as Barcelona-Real Madrid or Bayern Munich-Borussia Dortmund.
Bayern, beaten finalists last season when Chelsea lifted the trophy, and Serie A champions Juventus, back in the quarter-finals after a seven-year absence, both have commanding leads at the top of their respective leagues.
The Bavarians, at home in the first leg, hammered Juventus 4-1 won away when the teams last met three seasons ago, but Bayern chief executive Karl-Heirz Rummenigge was still cautious.
"That is certainly not a dream draw for us," he told reporters. "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."
Paris St Germain's sports director Leonardo immediately declared his side as underdogs after they were drawn with Barcelona.
"It couldn't have been worse for us in a purely sporting sense," the Brazilian, whose side are home in the first leg, told reporters. "Barcelona are almost the perfect team."
"We are starting a new project and it's our first year in the Champions League after a long time. We have to look on this as a football festival, an opportunity to measure ourselves against the best team in the world."
The Qatari-backed Ligue 1 leaders are set to be without former Barcelona striker Zlatan Ibrahimovic in the first leg as he completes a two-match suspension.
Barcelona sporting director Andoni Zubizarreta said his team cannot afford to slip up like they did in the last round, when they lost the first leg against AC Milan 2-0 before storming through with a 4-0 second leg win.
"We have just had an experience in the last round that should make us cautious," Zubizarreta told Spanish television.
"PSG ... are an experienced team who know how to play these kinds of matches, very competitive."
Galatasaray's clash with Real with will revive memories of their meeting in the 2000-01 season, also in the quarter-finals, when the Turks overturned a two-goal deficit at home to win 3-2. Real, who will play at home first this time, won the return 3-0.
"We need to get a very good result at home because we know that their fans will make it very difficult there," Real director Emilio Butragueno told Sky Sports.
Galatasaray assistant coach Umit Davala, who converted a penalty in that game, said he would have preferred a Bundesliga side because of Turkish support in Germany.
"I had been thinking of Borussia Dortmund," Davala, whose side beat Schalke 04 in the last round with a 3-2 win in the away leg in Germany, told Reuters.
"It's an advantage for us to play in Germany, there were around 18,000 Turks at the Schalke match."
"Both teams play attacking football and score lots of goals," added the former Turkey international. "Drogba and Wesley Sneijder have integrated well into our team and we are a team with a lot of character.
Dortmund sports director Michael Zorc, whose team are at home in the first leg, seemed relieved to get Malaga.
"We can live with this draw," he said. "At least it is better than playing Barcelona, Real or Bayern."
Malaga's achievement is even more remarkable after a turbulent summer which included reports that the clubs Qatari owner wanted to exit after only two years.
The first legs will be played on April 2 and 3 and the second legs one week later.
Malaga v Borussia Dortmund
Real Madrid v Galatasaray
Paris St Germain v Barcelona
Bayern Munich v Juventus
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- Borussia Dortmund
- Real Madrid