The so-called dieselgate emissions scandal first came to light in September 2015.
Munich prosecutors said they had acted because of a risk that Mr Stadler might seek to suppress evidence.
Audi's parent, the Volkswagen Group, confirmed that Stadler was detained this morning but that the "hearing to determine whether he will be remanded is ongoing".
The Munich prosecutor's office is reportedly working towards the investigation of 19 other suspects, identities of whom haven't been disclosed, yet.More news: Fans React To Phil Mickelson's Controversial Move At Shinnecock On Saturday
Stadler joined Audi in 1990, and became CEO in 2007.
A spokesman for Porsche SE, the company that controls VW and Audi, said Stadler's arrest would be discussed at a supervisory board meeting on Monday.
Munich prosecutors had conducted searches at Stadler's private residence as a part of the probe concerning alleged fraud and indirect improprieties with documents. Around 11 million vehicles from Audi are allegedly fitted with the emission manipulation devices.
Volkswagen has pleaded guilty to criminal charges in the United States and nine managers, including former CEO Martin Winterkorn, were charged there.