The Gunners conceded as many as three goals in the opening 45 minutes at the Allianz Arena in Munich in the Group F game.
Poland international striker Lewandowski put Bayern in the lead after just 10 minutes, and Germany international forward Thomas Muller made it 2-0 just before the half-hour mark mark.
David Silva put the German champions 3-0 up with a brilliant effort from long range on the stroke of half time.
Arsenal had just 32% of the possession, took one shot and failed to earn a single corner.
Hosts Bayern had 68% of the possession, took 15 shots of which 10 were on target, and earned four corners.
Former Newcastle striker Shearer is watching the match, and he is not impressed with the performance of Arsenal.