Freiburg substitute Nicolas Hoefler pounced at the far post to level the score in the 86th minute after Xherdan Shaqiri had fired the visitors ahead with a 33rd minute volley.
There was more bad news for Bayern as Bastian Schweinsteiger limped off 12 minutes from time with an ankle injury ahead of Friday's UEFA Super Cup match against Chelsea in Prague.
The treble winners have 10 points from four games. Borussia Dortmund, Bayer Leverkusen and Mainz 05, who all have nine points, are in action at the weekend. Freiburg have two points.
Bayern coach Pep Guardiola made seven changes to the team that beat Nuremberg 2-0 on Saturday for a match moved forward because of the showdown with Europa League winners Chelsea.
The Bavarians still controlled possession but were clearly lacking any spark with Arjen Robben, Philipp Lahm and Franck Ribery on the bench and Freiburg holding out well against them.
The visitors had to wait 33 minutes to take the lead when Shaqiri did well to control a cross from Thomas Mueller at the far post and drill home a powerful volley from a tight angle.
Freiburg came agonisingly close to an equaliser on the hour when 20-year-old Charles-Elie Laprevotte curled a shot on to the post in his Bundesliga debut.
But the home side's endeavours were finally rewarded four minutes from time when Hoefler snatched an unexpected leveller with Bayern's central defenders caught napping.
(Reporting by Karolos Grohmann; editing by Ken Ferris)
