Harry Kane (centre) made his Bayern debut less than 24 hours after joining
Only hours after completing his £86m move from Tottenham on Saturday, the striker came on as 64th-minute substitute to a huge cheer at the Allianz Arena.
He had only three touches and made little impact.
Dani Olmo scored a hat-trick for Leipzig to deny 30-year-old Kane the first trophy of his career.
Olmo's first goal was into the bottom corner after a cross was not cleared. His second was brilliant, spinning Matthijs de Ligt before slotting through Sven Ulreich's legs.
The Spain forward got his hat-trick with a penalty after Kane's introduction.
Bayern manager Thomas Tuchel said: "It is a big problem because it feels as if we had done nothing in the past four weeks.
"I cannot explain it. It was just not enough in every department. I have no idea why. There is no relation between our form and attitude going into the game and our performance on the pitch.
"It is the worst thing because there is such a big discrepancy."
Kane will have better days in Germany once he gets to know his new team. It was a slight surprise he was involved, having only become a Bayern player on the morning of the game.
He has scored 354 goals in his career and is the record scorer for Tottenham with 280, and England with 58.
Leipzig's performance was especially impressive considering they lost three of their leading players to the Premier League this summer.
Croatia defender Josko Gvardiol joined Manchester City for £77m, Hungary midfielder Dominik Szoboszlai went to Liverpool for £60m and France striker Christopher Nkunku moved to Chelsea for £52m.
The German Super Cup is the equivalent of the Community Shield in England, with Bayern the Bundesliga champions and Leipzig the German Cup winners.
Bayern beat Leipzig 5-3 to win last season's German Super Cup.
-- Courtesy of BBC Sport