"Due to his ongoing pretrial detention, he is unable to fulfill his duties as a member of the board of management and wishes to concentrate on his defense," the statement said of Stadler.
Volkswagen previously said that Stadler would be considered innocent until proven guilty. Audi tapped its top sales executive to lead the company after Stadler was detained.
The German carmaker has admitted that it rigged millions of diesel engines to cheat on emissions tests.
Diesel cars from Volkswagen and its Audi subsidiary cheated on clean air rules with software that made emissions look less toxic than they actually were.
The scandal sent its share price plunging, and trashed confidence among consumer and regulators in diesel technology. The episode has already cost Volkswagen more than $30 billion in recalls, legal penalties and settlements.
In a separate announcement on Tuesday, Volkswagen said it would offer incentives to customers in Germany who wanted to swap older diesel cars for cleaner models.
Diess acknowledged at a press conference in April that Volkswagen had "lost a great deal of trust," and that it would take years to restore public confidence in the automaker.