German conservative Mueller, 69, who served a five-year posting as head of the powerful department responsible for church doctrine, the Congregation for the Doctrine of the Faith (CDF), had clashed with the pope over key reform issues.
Vatican mulls excommunicating mobsters and the corrupt
He was one of several cardinals who questioned Francis's determination for the Catholic Church to take a softer line on people traditionally seen as "sinners", including remarried divorced people who want to take Communion.
Mueller had also been caught up in the controversy surrounding the Church's response to the clerical sex abuse scandal after his department was accused earlier this year of obstructing Francis's efforts to stop internal cover-ups of abuse.
Pope tells Merkel to keeppressing for international cooperation
The Vatican said Mueller's five-year term would not be renewed and he would be replaced by CDF Secretary Archbishop Luis Francisco Ladaria Ferrer, a 73-year-old Spaniard.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ