Barca’s rampant strikeforce did the damage in a completely one-sided first half.
The Catalans raced into a two-goal lead within 12 minutes as Lionel Messi and Samuel Eto’o struck early on.
And the locals’ dominance brought two more goals before half-time, with Thierry Henry setting up Messi for his second seven minutes before the break and then slotting home a fourth himself just before the interval.
Bayern had advanced to the quarter-finals in style, thrashing Sporting Lisbon 12-1 on aggregate to seal a spot in the last eight.
But Jurgen Klinsmann’s side have been less impressive in the Bundesliga.
They came into this match in fourth place and on the back of a humiliating 5-1 defeat at Wolfsburg on Saturday.
With Xavi and Andres Iniesta pulling the strings in midfield and Messi, Eto’o and Henry causing havoc up front, Pep Guardiola’s side soon took control of the game.
Barca went in front. as they tore the visitors’ defence apart with a flowing move and Eto’o set up Messi, who drilled a neat finish past Hans-Jorg Butt to open the floodgates.
And three minutes later, Messi returned the compliment as he slid a deadly ball into the path of Eto’o and the Cameroon striker clinically slotted past the helpless Butt.
France striker Henry was a constant threat to the Bayern defence and he set up Barca’s third seven minutes before the break.
Henry beat his marker for pace on the left and flashed a low centre across the six-yard box which Messi poked home with his outstretched right leg to give Barcelona a three-goal lead.
And two minutes before the break, the Catalans scored again.
Messi charged in from the right flank and laid the ball off to Eto’o, who in turn found Henry and the unmarked Frenchman slid a low angled drive into the bottom right-hand corner to virtually seal Barca’s passage to the semi-final within just 45 minutes.
Bayern were also lucky not to go down to 10 men as former Barca midfielder Mark Van Bommel got away with a cynical elbow on Messi just before Henry slotted home.
And their dominance continued after the interval.
Messi’s shot was pushed onto the woodwork by Butt just short of the hour-mark and Iniesta drilled an effort wide of the target with 12 minutes left.
In truth, Bayern had not been in the game and a goal would have been flattering to the Germans.