The run, a record across Europe's top five leagues, has immediately installed Bayern among the favourites for a potential treble.
Domestically, the reigning Bundesliga champions sit comfortably atop the table after ten matches, boasting nine wins and a single draw.
Their near-perfect form has opened up a significant points lead over their closest rivals, with Kompany's side displaying both attacking flair and defensive steel.
Club president Herbert Hainer has been delighted by the Bavarians' season to date, and credited their togetherness and team spirit for the success.
"We have a great team spirit and togetherness thanks to the coach. Of course we have brilliant individual players, but the togetherness of the team is the merit of the coach," Hainer told Sky Germany.
"The team is motivated to the core, everyone is fighting for each other - you can see it when Harry Kane is back defending in his own box, that's how it should be."
In the DFB-Pokal, Bayern cruised past FC Koln with a 4-1 victory in the Second Round to book their place in the Round of 16, where they will face Union Berlin. Their only setback so far came in the Franz Beckenbauer Supercup, where they fell 1-2 to VfB Stuttgart in August.
On the European stage, Bayern have impressed in the UEFA Champions League league phase, topping their group with convincing wins against several elite opponents.
Harry Kane has been the standout performer, scoring 13 goals and providing three assists, supported ably by Luis Díaz (six goals, four assists) and Michael Olise (four goals, three assists). Their attacking trio has been central to Bayern's dominant form and growing momentum.
Vincent Kompany admits replacing Michael Olise will not be easy after the winger's display helped Bayern Munich secure a commanding advantage in their Champions League tie against Atalanta.
Luis Diaz was both hero and villain for Bayern Munich in the Bundesliga on Saturday as he scored the equaliser before being sent off as the Bavarians drew 1-1 with Bayer Leverkusen at the BayArena.
Bayer Leverkusen return to Bundesliga action on Saturday as hosts to leaders Bayern Munich, still grappling with inconsistency that threatens their top-four ambitions.
Bayern Munich delivered a commanding 6-1 victory over Atalanta BC in the first leg of their UEFA Champions League round-of-16 tie on Tuesday, but the emphatic result was clouded by injuries to Alphonso Davies, Jamal Musiala and Jonas Urbig.
