It was the Spanish giants' worst Champions League defeat since the 4-0 loss to Dynamo Kiev in the group stage in 1997.
Germany star Thomas Müller was Barca's chief tormentor with a goal in each half while striker Mario Gomez and Dutch winger Arjen Robben also netted to give Bayern a huge advantage for the return leg at the Camp Nou on May 1.
Barcelona assistant coach Jordi Roura admitted his team would need a near miracle to now reach their third Champions League final since 2009.
"Miracles are always hard to make real, 4-0 is a huge deficit to make up," said Roura. "I don't know if anyone has come back from a score like that in the history of the Champions League, but we'll do what we can. This is a big defeat which hurts us a lot."
"They thrashed us," admitted Barca defender Gerard Pique. "It is almost impossible, but we have to show face in the return leg."
In contrast, Bayern, who are bidding to become the first German team to win a treble of European as well as domestic league and cup titles, were buoyant.
"That's crazy, hard to believe," said Robben. "They've dominated Europe in the last few years and and then we go and win 4-0. The key was we fought and defended together."
But Bayern coach Jupp Heynckes warned the job is only half done.
"Of course, we're all very happy about the win, especially the size of the margin. We were first-class," he said. "But we know we still have 90 minutes ahead of us in Spain. We want to enjoy tonight, but nothing more."
An exceptional day for Bayern got off to an unusual start when it was announced they had signed young Germany star Mario Götze from arch-rivals Borussia Dortmund for a reported €37 million ($48.1 million).
Then it was reported that, in March, club president Uli Hoeneß, caught up in a tax evasion scandal, was arrested and released on bail after a police raid on his home, but he was at the Allianz Arena to witness an incredible night.
Barcelona's Argentine superstar Lionel Messi started, despite struggling with a hamstring injury since the start of the month, but the World Player of the Year was a shadow of his usual self.
Bayern had an early penalty appeal turned down, but the hosts went ahead when Robben's lobbed cross from a corner was headed across goal by centre-back Dante for Mueller to place his header inside the far post on 24 minutes.
Dante came to his side's rescue at the other end five minutes later to get a toe to a Pedro Rodríguez cross from the right that was heading straight for Messi at the back post.
And Bayern doubled their lead in the 49th minute as Gomez struck with his sixth goal in his last three games.
Again, the Barcelona defence failed to deal with a corner as Robben's ball from the right was nodded down by Müller for Gomez to volley home on 49 minutes.
Dutchman Robben, who had been a constant menace to the Barca defence, grabbed the third on 73 minutes, skipping past Jordi Alba on the right before sliding his shot past Victor Valdes from a tight angle.
However, the Barcelona players were furious and protested to the referee as Alba had been body-checked by Müller as he chased Robben inside the box.
"The referee didn't have an influence," admitted Pique after. "They were just quicker, stronger, better."
With the Barcelona defence in a shambles, Bayern grabbed the fourth on 82 minutes when Franck Ribery and David Alaba combined on the left for the latter to whip in a low ball which Müller slid into the net for his second.
Despite the advantage, Bayern know how tough life could be at the Camp Nou, having lost 4-0 on their last Champions League visit to Barcelona in the 2009 quarter-final, first leg which they went on to lose 5-1 on aggregate.