And Arsenal will take on tournament favourites and holders Barcelona in the last eight after today's draw in Nyon.
United beat Bayern in dramatic fashion at the Nou Camp 11 years ago, scoring twice in the dying minutes to complete an historic treble.
Night to remember: United beat Bayern 2-1 in the 1999 Champions League final
Sir Alex Ferguson's side thrashed AC Milan in the previous round and will be confident of progressing to the semi-finals, where they will face the winner of the all-French clash between Lyon and Bordeaux.
United will be at home in the second leg, but Arsenal are at home first to Barcelona. Arsenal boss Arsene Wenger will no doubt have wanted to avoid Barca in today's draw, but Cesc Fabregas will relish playing against his former club, with whom he is often linked with a return.
It will also mark Thierry Henry's first return to Arsenal, after he left the club in the summer of 2007. It is set to be an emotional return to the Emirates for the striker, who scored 226 goals for the north Londoners.
QUARTER FINAL DRAW First Legs to be played 30-31 March:
LYON v BORDEAUX BAYERN MUNICH v MANCHESTER UTD ARSENAL v BARCELONA INTER MILAN v CSKA MOSCOW Second Legs to be played 6-7 April
In an interview last month, the France international admitted he dreaded the idea of facing his former club.
'I'll be an Arsenal fan until I die and if you ask me how that makesme feel about the possibility that Barcelona might meet Arsenal in thenext round of the Champions League should we both qualify, I have tosay I find the idea unthinkable,' he told The Times.
'It's always the same on the day of a Champions League draw. Until Isee that Arsenal have been paired with another team, I can't breathe.
Cesc appeal: Arsenal were beaten by Barcelona in Paris back in 2006
'Proud though I am to be a Barcelona player, I dread the thought ofhaving to oppose Arsenal. I would hate it. I pray for it not to happen.'
The winner of the clash between Arsenal and Barcelona will faceeither Inter Milan - who knocked out Chelsea earlier this week - orCSKA Moscow in the semi-finals.
The first leg of the quarter-finals will be played on March 30 or 31, with the return leg on April 6 or 7.
SEMI FINAL DRAW First Legs to be played 20-21 April
Bayern Munich/Man Utd v Lyon/BordeauxInter Milan/CSKA Moscow v Arsenal/Barcelona Second Legs to be played 27-28 April
Bayern chairman Karl-Heinz Rummenigge labelled the tie a 'tough butattractive draw', although he admits United will be expected to gothrough to the last four.
'Manchester are a team who are ranked right at the top,' he said on his club's website.
'We will have to push ourselves to our limits and possibly even beyond to go through.
'Manchester are the favourites, but that is where the attraction lies, to try to beat a favourite.'
Former United striker Dwight Yorke, who played in the ChampionsLeague final in 1999, told Sky Sports News: 'I'm worried about theGermans, over the years they've been very difficult to play against.
French connection: Henry celebrates winning the 2004 Premier League title at White Hart Lane with Vieira
'They've got a very experienced manager in Louis van Gaal, he's beenaround the block, he knows how European football is, he knows aboutEnglish football and will certainly know about Manchester United andWayne Rooney.
'But the reason why I'm pretty confident that Man United will advance is the second leg will be played at home.
'Going away they will have to be very cautious. Bayern Munich are very hard to play against, they are tactically sound, they don't take too many chances, they'll wait for that opportunity to pounce on you.'
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