Bayern win 3-2 on aggregate
Thierry Henry's second-half strike was not enough to prevent Arsenal crashing out of the Champions League.
Henry fired a powerful drive past Oliver Kahn after 65 minutes, but Arsenal could not grab the second goal that would have sunk impressive Bayern.
Arsenal struggled to break Bayern down, even though Kahn was also forced to save brilliantly from Kolo Toure's header with only two minutes left.
Bayern's Michael Ballack brought a fine second half save from Jens Lehmann.
Arsenal recalled Dennis Bergkamp, but his only impact on a first 45 minutes dominated by Bayern was a cynical challenge on Lucio that deservedly brought a booking.
Bayern dominated possession and territory, although they struggled to carve out clear-cut opportunities.
There was a moment of alarm for Arsenal on the half-hour when goalkeeper Jens Lehmann was caught out of position, but he regained ground to claim Sebastian Deisler's lob.
Henry represented Arsenal's best attacking threat, and he brought a fine block out of Oliver Kahn at his near post after a trademark surging run five minutes before the interval.
Arsenal upped the tempo after the break, and Patrick Vieira was unlucky after 54 minutes, following up some neat control with a shot that flew across the face of the goal.
Boss Arsene Wenger was desperate to make the breakthrough, and made a double change after 62 minutes, sending on Robert Pires and Cesc Fabregas for Mathieu Flamini and the bitterly disappointing Jose Antonio Reyes.
And they finally broke Bayern down three minutes later, inevitably courtesy of a moment of brilliance from Henry.
He controlled Ashley Cole's long ball in an instant before beating Kahn with a left-foot finish.
Bayern steadied themselves, and it required a stunning save from Lehmann to keep the Germans at bay with 16 minutes left, diving acrobatically to turn over a shot from Michael Ballack.
Kahn then denied Toure as the seconds ran out, leaping to turn over his powerful header.
The quarter-final draw will take place on Friday 18 March. Any team can be drawn against another and the two legs will be played on 5/6 and 12/13 April.
Arsenal: Lehmann, Lauren, Toure, Senderos, Cole, Ljungberg (Van Persie 80), Flamini (Fabregas 63), Vieira, Reyes (Pires 63), Bergkamp, Henry.
Subs Not Used: Taylor, Silva, Clichy, Owusu-Abeyie.
Booked: Bergkamp, Toure, Fabregas.
Goals: Henry 66.
Bayern Munich: Kahn, Sagnol, Lucio, Kovac, Lizarazu, Demichelis, Salihamidzic (Hargreaves 90), Deisler (Ze Roberto 72), Ballack, Guerrero (Linke 85), Pizarro.
Subs Not Used: Rensing, Hashemian, Jeremies, Schweinsteiger.
Booked: Demichelis, Salihamidzic, Ballack, Lizarazu.
Ref: Massimo De Santis (Italy).