The 19-year-old will return to his parent club at the end of the current campaign.
More match practice
"The contract's a clear sign to Pierre-Emile Hojbjerg that he's a part of Bayern's future," explained sporting director Matthias Sammer. "The loan deal's a good move for him to get more minutes under his belt and then come back to us."
The Danish international has made eight Bundesliga appearances so far this season, as well as a further three in the group stages of the UEFA Champions League.