New Bayern manager Nagelsmann will take his team to Leipzig in the fourth round of the campaign, on the weekend of September 11-12, having chosen to leave the Saxony club to join the champion.
Nagelsmann, who has replaced Hansi Flick in the Bayern top job, will be expected to keep up the high levels of success the Bavarians have enjoyed in recent years.
Bayern won the league by 13 points last season, with Leipzig finishing second and Borussia Dortmund taking third place.
Bayern will host Leipzig on the weekend of February 4-6, the 21st matchday of a 34-game campaign that is due to wrap up on May 14.
Leipzig and Dortmund are again expected to be in the hunt for silverware in the new campaign, yet toppling Bayern could be a tall order as they attempt to extend their record-breaking streak of championships.
Last season's top three will all have new coaches in 2021-2022, with Nagelsmann at Bayern, Jesse Marsch coming in at Leipzig and Marco Rose moving from Gladbach to Dortmund.
Bayern opens at Monchengladbach on Saturday, 14 August (AEST), while Dortmund will host Eintracht Frankfurt on the same weekend and Leipzig travels to face Mainz.
Nagelsmann will take charge of Bayern in Der Klassiker for the first time when they face Dortmund at Signal Iduna Park on the weekend of December 3-5, ahead of the final round of Champions League group matches.
The return fixture in that great rivalry sees Dortmund visit the Allianz Arena on the weekend of April 22-24.
The clashes between Leipzig and Dortmund could be telling in terms of who mounts the most serious challenge to Bayern, and Leipzig will have home advantage in their first meeting (November 5-7), with the return game set to take place on the weekend of April 1-3, as the season heads towards its decisive stage.