Kane, who is a lifelong supporter of Tottenhamand the club's all-time leading scorer with 280 goals in 435 appearances, gave Bayern the lead after 12 minutes with a composed finish inside the penalty area.
The England captain then had an opportunity to double Bayern's advantage two minutes later when Joao Palhinha, who transferred to Spurs from Bayern on a season-long loan on Sunday, conceded a penalty.
Kane, however, slipped, sending his shot soaring over the crossbar. This was the first occasion Kane missed a penalty since his failure in the 2022 World Cup quarter-final against France.
Kingsley Coman added the second goal for the home team with a brilliant curling shot from the edge of the box after 61 minutes.
Bayern's young players Lennart Karl and Jonah Kusi-Asare both found the net in the closing moments to seal the one-sided win.
The match was the Europa League champions' final opportunity to prepare before next Wednesday's UEFA Super Cup showdown with European titleholders Paris Saint-Germain.
Spurs have had a mixed pre-season under new coach Thomas Frank, securing victories against London rivals Arsenal and Reading, while drawing with Newcastle, Luton Town and Wycombe.
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