The match, which took place at the Russian Railways Arena stadium in Moscow, ended with a score of 2: 1 in favor of the guests.
Leon Goretzka and Josua Kimmich scored at Bayern.
The only goal was scored by Anton Miranchuk.
Bayern have six points after two rounds and lead Group A. Lokomotiv has one point and second place, but the match between the other two teams of the quartet, Atlético and Salzburg, will be played later.
Earlier it was reported that Lokomotiv footballer Magkeev was injured during a warm-up before the Champions League match with Bayern Munich.