The club issued a statement on Thursday saying performances this season had failed to live up to expectations with CEO Karl-Heinz Rummenigge pinpointing Wednesday's defeat in Paris as evidence of the team's struggles.
Bayern, who have won the last five consecutive Bundesliga titles, are currently in third place in the Bundesliga, three points off leaders Borussia Dortmund.
They threw away a two-goal lead to draw 2-2 against VfL Wolfsburg last week, however, having also suffered a surprise defeat at Hoffenheim earlier this month.
Italian Ancelotti joined last season, succeeding Pep Guardiola, and enjoyed immediate success, winning the Bundesliga title in his debut campaign.
His side, however, were less successful in Europe and were eliminated in the quarter-finals of 2016/17 Champions League by eventual winners Real Madrid.
Frenchman Willy Sagnol, Ancelotti’s assistant who joined this season, will be taking over on an interim basis and will be in charge on Sunday against Hertha Berlin, Bayern said.
"The performances of the team since the season start did not correspond to the expectations," said Rummenigge.
"The Paris match showed clearly there needed to be consequences. (Sports director) Hasan Salihamidzic and myself informed Carlo today of our decision in an honest and serious discussion...
"Carlo is a friend of mine and will remain so but we had to take a professional decision for Bayern Munich. I now expect from the team a positive development and absolute passion so that we reach our goals."
The 58-year-old Ancelotti, who has also coached Real Madrid, Juventus, AC Milan and Chelsea among others, has been criticised for a number of his decisions this season, including frequently keeping forward Thomas Mueller on the bench.
He also left Franck Ribery and Arjen Robben, his two most experienced wingers, on the bench at the start against PSG in a tactical decision that swiftly backfired.
PSG took the lead after two minutes through Dani Alves and added further goals from Edinson Cavani and Neymar.
(Reporting by Karolos Grohmann; Editing by Toby Davis)
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