Kane, who is boyhood club Tottenham's all-time top goalscorer with 280 strikes in 435 matches, put Bayern in the lead after 12 minutes with a composed penalty box finish.
The England captain then had a chance to double Bayern's lead two minutes later when Joao Palhinha, who joined Spurs from Bayern on a season-long loan on Sunday, gave away a penalty.
Kane, however, slipped, blasting his shot well over the bar. It was the first time Kane failed to convert a spot kick since his miss in the 2022 World Cup quarter-final defeat to France.
Kingsley Coman added the home side's second with a superb curling shot from the edge of the box with 61 minutes gone.
Bayern teenagers Lennart Karl and Jonah Kusi-Asare both scored in the dying stages to complete the one-sided victory.
The match was the Europa League winners' last chance to fine-tune before next Wednesday's UEFA Super Cup clash with European champions Paris Saint-Germain.
Spurs have had a mixed bag under new coach Thomas Frank this pre-season, beating London rivals Arsenal along with Reading, while being held to draws with Newcastle, Luton Town and Wycombe.