Greuther will take on the record champions on the weekend of August 25-26 after the fixtures for the new season were announced on Tuesday.
Defending champions Borussia Dortmund play the first game of the season, at home to Werder Bremen on Friday August 24.
The other newly-promoted sides, Eintracht Frankfurt and Fortuna Dusseldorf, start their campaigns at home to Bayer Leverkusen and away to Augsburg respectively.
Bayern take on Dortmund for the first time at the Allianz Arena in the15th round of fixtures between November 30 and December 2.
The reverse fixture will be the third last game of the season between May 3 and 5.
Dortmund finish the season on May 18 at home to Hoffenheim and Bayern away to Borussia Monchengladbach.