Dani Alves, Edinson Cavani and Neymar scored the goals that brought a second consecutive victory to Unai Emery's expensively assembled outfit in this season's Uefa Champions League.
Bayern's defeat leaves them second in Group B with three points. PSG, who boast six points, have scored eight goals and conceded none in their their two fixtures.
Domestically, Bayern are third in the Bundesliga after six games, three points adrift of leaders Borussia Dortmund. Bayern have not been so far off the pace so early in a season since 2010/11 when Dortmund - led by Jurgen Klopp - clamed the title and Bayern finished third.
"The performance of our team since the start of the season has not met the expectations we put to them," said Bayern's chief executive Karl-Heinz Rummenigge.
"I would like to thank Carlo for his cooperation. Carlo is my friend and will remain my friend. But we had to make a professional decision. The game in Paris clearly showed that we had to draw consequences."
Ancelotti, 58, took over at the Allianz Arena in the summer of 2016 from Pep Guardiola who left to manage Manchester City. The Italian emulated the Spaniard by delivering the Bundesliga - their fifth on the trot - but he was unable to secure the German Cup like Guardiola's teams of 2014 and 2016. There was also no improvement on Guardiola's record in the Champions League.
Ancelotti is one of only seven men to have won European football's most prestigious competition as a player and as a coach. He was a midfielder in the AC Milan sides that claimed back-to-back European Cups in 1989 and 1990. As a coach he led Milan to the 2003 and 2007 Champions League titles. He steered Madrid to their 10th overall success in the event in 2014.
Bayern play on Sunday in the Bundesliga at eighth placed Hertha Berlin. Assistant manager Willy Sagnol - a former Bayern defender - will lead the side.
"I now expect the team to have a positive development and top performance, so we can reach our goals for this season," added Rummenigge."