The Gunners put in a spirited first-half display as they looked to overturn a 5-1 deficit from the first leg three weeks ago and deservedly took the lead through Theo Walcott (20) and they could have even had a penalty when the England international went down under a challenge from Xabi Alonso.
But things unravelled for the Gunners early in the second half when Laurent Koscielny brought down Robert Lewandowski in the penalty area. The Frenchman was initially shown a yellow card but that was upgraded to a red much to the disbelief of the Arsenal players.
The 5-1 defeat is the biggest Arsenal have suffered at the Emirates and piles even more pressure on Wenger's position at the club.
Arsenal will look to avoid further embarrassment when they take on non-league Lincoln in the quarter-final of the FA Cup on Saturday, while Bayern await the draw for the next round which will take place on March 17.