Stadler is the most senior Volkswagen to be arrested over the so-called Dieselgate that came to light in 2015.
Just last week, Volkswagen agreed to pay a 1 billion-euro fine imposed by German prosecutors for cheating to get around diesel-emissions regulations.
Audi and Volkswagen confirmed that Stadler was detained on Monday and said he still had a presumption of innocence.
The reason for the arrest was because of a possible risk that he could suppress evidence in the ongoing investigation of alleged fraud and false advertising, according to the Munich prosecutors office, stated a Reuters report.
The Munich prosecutors said Stadler's arrest was not made at the behest of USA authorities.
Fernando Alonso helps Toyota win 24 Hours of Le Mans
It was the No. 8 vehicle of Fernando Alonso , Kazuki Nakajima, and Sébastien Buemi that took the checkered flag. Jenson Button, the 2009 F1 world champion, was competing in the non-hybrid LMP1 class for the Russian SMP team.
The Munich prosecutor's office is reportedly working towards the investigation of 19 other suspects, identities of whom haven't been disclosed, yet.
As part of the investigation, Stadler's home has been raided, while authorities are now investigating 19 other suspects, the identities of whom have not been disclosed.
Audi has also been embroiled in the emissions scandal that has plagued Volkswagen.
Volkswagen admitted that almost 600,000 cars sold in the United States were fitted with "defeat devices" created to circumvent emissions tests.
The auto manufacturer pleaded guilty to criminal charges in the United States and nine managers, including former CEO Martin Winterkorn, were charged.