The German side opened the scoring in only the seventh minute, with Toni Kroos drilling a half-volley past Wojciech Szczesny from the edge of the box.
© AP Photos
Arsenal were rocked by the early goal and were unable to create any clear opportunities to trouble the visiting defence.
Arsenal improved towards the end of the first period but their attacking intent was met with some stubborn resistance by a well organised Munich defence.
However, it was the visitors who could have had the final say before the interval when Mario Mandzukic found space in the area but the forward headed the ball agonisingly wide of the target.