Marcus Rashford's first appearance since the World Cup failed to inspire Jose Mourinho's men, who were outclassed and starved of possession in their last friendly before Friday's Premier League opener at home to Leicester City.
The slim margin of defeat owed only to the admirable resilience of a defence that was reinforced by the presence of Victor Lindelof and substitute Phil Jones, although the ease with which Javi Martinez rose to nod home Thiago Alcantara's 59th-minute corner will be of concern.
But the more pressing matter for Mourinho is clearly at the other end of the pitch, where an attack shorn of Romelu Lukaku, Jesse Lingard and Anthony Martial never looked like scoring.
It was a subdued performance from the outset with the earliest drama seeing Alexis Sanchez, United's captain on the night, catch Joshua Kimmich in the face with a stray arm.
It was to be the only blow the visitors landed throughout the opening half as a comfortable Bayern asked questions of David de Gea through Thiago, Serge Gnabry and Niklas Sule, who was compelled to try his luck from long range after advancing unimpeded out of his own defence.
Manuel Neuer, in contrast, did not have a save to make in his first 45 minutes at Allianz Arena since a 4-0 win over Mainz on September 16, his final club outing before foot surgery curtailed much of his campaign.
Niko Kovac showed little interest in settling at half-time with Jerome Boateng, Robert Lewandowski and Leon Goretzka introduced off the bench, yet the goal came from an unlikely source as midfielder Martinez calmly guided a glancing header beyond a helpless De Gea.
Arjen Robben looked to have made it 2-0 late on but was correctly flagged for offside as the Bundesliga champions earned their second win in four ahead of next Sunday's DFL Supercup clash with Eintracht Frankfurt.
What it means: United in defence
Jose Mourinho, successful or otherwise, appears intent on making United the tactical counterpoint to their Premier League rivals.
In the absence of many first-team regulars, Mourinho's men sat deep in a passive performance, which was a departure from the earlier scenes at Wembley Stadium, where Manchester City and Chelsea both employed high presses to varying degrees of success in the Community Shield.
Bayern, meanwhile, are evidently not yet at their swashbuckling best, having failed to engineer a way through a static back four before Martinez's intervention.
Pat on the back: Classy Sule
Bayern look to have a readymade replacement for Jerome Boateng should the Germany international join Paris Saint-Germain as has been heavily rumoured. Sule was full of confidence on the back of his World Cup involvement, dealing ably with rare moments of danger and exuding belief in stepping out of defence.
Boot up the backside: Sanchez out of sorts
Alexis Sanchez, albeit constrained by a cagey United approach, was some distance short of the explosive bundle of energy to which we have become accustomed as he remained isolated on the left flank.
Bayern's bid for another season full of silverware begins with the DFL Supercup against Eintracht - Niko Kovac's former club - next Sunday, while United welcome Leicester City to Old Trafford in the Premier League's opening fixture in five days' time.