The Gunners arrived in Germany with an unbeaten record and having not conceded a single goal in the competition.
Eberechi Eze opened the scoring with a fierce low drive past Manuel Neuer in the first half.
Declan Rice burst into the area to slam in the equaliser for Arsenal, to ensure that the Premier League champions left Munich with a point.
In the other matches played on the night, Real Madrid thrashed RB Leipzig 4-1, Galatasaray won 4-2 at Lille and Como beat Manchester United 4-1.
Real Betis edged Feyenoord 1-0, LASK stunned Sporting 3-2 and Aston Villa thrashed Viking 3-1 at Villa Park.
