The 20-year-old Danish international, who has been at the club since 2012, has struggled to win a spot in a crowded midfield for some time and also spent the second half of the 2014-15 season with Bundesliga rivals Augsburg.
"This is a solution which is good for all three sides," said Bayern sports director Matthias Sammer in a statement.
"We still have high hopes for Pierre-Emile Hojbjerg and see his future in Munich. In order to develop further he needs match practice and he will get that at Schalke."
(Reporting by Karolos Grohmann; Editing by Tony Jimenez)
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