Kane scored a second-half hat-trick in a 3-0 home win over Augsburg which sent Bayern Munich eight points clear on Friday, bringing up his Bundesliga half-century in 43 games.
The England captain beat the previous record set by Manchester City's Erling Haaland in 2021, then at Borussia Dortmund, who reached his half century in 50 games.
Kane's hat-trick was his seventh in the league since arriving in the summer of 2023.
Two of Kane's three goals on Friday came from the spot and he has now scored 25 consecutive penalties for club and country in all competitions since missing against France in the 2022 World Cup quarter-finals.
The milestone comes after the 31-year-old was criticised during the international break, with some saying he should step aside for Aston Villa's Ollie Watkins.
Kane, who was also criticised for some lethargic performances at Euro 2024, told reporters he was "used to that now", adding he was "experienced enough to know that comes with being one of the top players, one of the top strikers."
Saying he felt "in the best form of his career", Kane said "all I can do is do my talking on the pitch, like I did tonight."
He said he was yet to talk to incoming England coach Thomas Tuchel, who also lives in Munich, but said "I'm sure we'll have a conversation on the experiences I've had, the good and bad things, and what we can improve."
