Dortmund open Bundesliga season
Greuther will take on the record champions on the weekend of 25-26 August 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 24 August.
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 the 15th round of fixtures between 30 November and 2 December. The reverse fixture will be the third last game of the season between 3 and 5 May.
Dortmund finish the season on 18 May at home to Hoffenheim and Bayern away to Borussia Monchengladbach.