The prosecutor could not comment further due to ongoing investigations.
The Munich prosecutors said Stadler's arrest was not made at the behest of USA authorities.
The emissions investigation was launched in 2015, when US regulators found that Audi had implanted illegal software devices into millions of its diesel-fueled vehicles to cheat emissions tests.
Audi has been caught up in the diesel emissions scandal that has plagued VW.
The directors of Audi and Volkswagen discussed how to run its more profitable division without Stadler, but failed to come to a conclusion, the carmaker said late on Monday. The company has earmarked more than €27bn in fines, buybacks and costs.
"As part of an investigation into diesel affairs and Audi engines, the Munich prosecutor's office executed an arrest warrant against Mr Professor Rupert Stadler on June 18, 2018", the prosecutor's office said in a statement. Stadler was given more responsibility over group sales in April when Volkswagen named Herbert Diess as its new chief executive. Another high profile figure under scrutiny in the diesel scandal is former Volkswagen CEO Martin Winterkorn, who was indicted in May on charges of conspiracy and fraud related to the emissions cheating.
It remains to be seen how long Stadler remains in police custody and whether he's able to remain in his post during his detention. He has been CEO since 2007, and a member of the Volkswagen board since 2010.
Last month, Germany's Motor Transport Authority ordered Audi to recall and fix 60,000 A6 and A7 diesel cars alleged to have the illegal software installed.
But investigations are continuing elsewhere.
Volkswagen said it would accept the fine imposed by prosecutors in the German city of Braunschweig.
VOLKSWAGEN on Monday is expected to announce a new head of its Audi luxury vehicle division after its current chief executive overnight was arrested in Germany over the Dieselgate scandal.
Both Audi and Volkswagen Group, which owns the luxury auto brand, are yet to issue a statement.