Stadler was arrested in mid-June as part of a broader probe into emissions cheating at the premium brand, which is part of Volkswagen Group.
He is being held at a prison in the Bavarian city of Augsburg. A Munich court now needs to review his appeal.
Stadler initially cooperated with prosecutors but has now stopped giving statements, the prosecutor's office said.
Munich prosecutors are probing Stadler and another member of Audi's top management for suspected fraud and false advertising tied to illegal pollution levels in its cars and manipulated vehicle tests.
Audi named sales executive Abraham Schot as an interim replacement with immediate effect after Stadler was detained.
(Reporting by Alexander Huebner; Writing by Edward Taylor; Editing by Douglas Busvine/Keith Weir)
