In a statement, Audi said it had “accepted the request” of Mr Stadler “to release him from his duties.”
It added: “The release is a temporary measure, put in place until the circumstances surrounding Stadler’s arrest have been clarified.”
Mr Stadler has been detained by German authorities investigating the “dieselgate” scandal at parent firm Volkswagen.
Prosecutors in Munich said Stadler – the most senior group official to be held since the emissions saga began almost three years ago – was arrested at home in the early hours following a search of the property last week.
They said his detention was linked to fears he might obstruct their continuing investigation, adding that he had been remanded in custody by a judge.
Audi responded by insisting there was a presumption of innocence in the case involving Mr Stadler, who has led the Audi division since 2007.