Stadler has been under fire since Audi admitted in November 2015 - two months after parent VW - that it also installed illegal "defeat device" software to cheat USA emissions tests.
Stadler is the most senior Volkswagen to be arrested over the so-called Dieselgate that came to light in 2015.
The Munich prosecutors said Stadler's arrest was not made at the behest of USA authorities.
Earlier this month, Munich prosecutors widened their probe at Audi to include Stadler and another member of Audi's top management, investigating them for suspected fraud and false advertising.
Audi CEO Rupert Stadler has been arrested.
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She performed a duet of Williams' smash-hit Angels with the Stoke-born singer, who also closed the ceremony with the hit. For his set, Williams delivered his song " Let Me Entertain You ", decked out in a red and black, animal-printed suit.
The arrest of the Audi CEO comes just weeks after Volkswagen tapped a new CEO to move the company past the scandal.
Volkswagen has pleaded guilty to criminal charges in the United States and nine managers, including former CEO Martin Winterkorn, were charged there.
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.
"The suspect has been seen by a judge, who has ordered him to be remanded in custody", the prosecutors' office said in a statement, published by Reuters.
Standler's home was raided last week where Munich prosecutors based the arrest warrant on concealment of evidence. The major auto group had admitted to equipping roughly 11 million vehicles worldwide with a "cheating software" that was created to illegally pass pollution tests. According to reports, the entire scandal has taken a heavy toll on the German auto manufacturers as it has cost it about 25 billion euros in buybacks, compensation and regulatory fines.