The company said that it couldn't comment further due to the ongoing investigation, but stressed that "the presumption of innocence remains in place for Mr. Stadler".
Stadler is the most senior Volkswagen to be arrested over the so-called Dieselgate that came to light in 2015.
Volkswagen has pleaded guilty to the criminal charges pressed against the company where two managers are serving prison time in US.
Audi has been caught up in the diesel emissions scandal that has plagued VW. The prosecutors also said that the arrest of Stadler was essential as the investigators saw the risk of him trying to suppress evidence in the diesel emissions probe.
Prosecutors in Munich, Stuttgart and Braunschweig are continuing their investigations of the vehicle maker and its units.
The Munich prosecutors said Stadler's arrest was not made at the behest of USA authorities.
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Former VW chief executive Martin Winterkorn stepped down soon after the scandal broke in September 2015, while successor Matthias Mueller was hastily replaced earlier this year.
German prosecutors had earlier confirmed that an arrest warrant issued to his name is based on "concealment of evidence" after conducting a raid at his house last week. The executive was arrested at his home in Ingolstadt in the early hours on Monday, they said.
Volkswagen shares were down 2.1 per cent at 157.66 euros in Frankfurt trading.
Munich prosecutors are investigating whether Stadler acted swiftly enough to stop deliveries of manipulated Audi models in Europe once emissions problems had emerged, a person familiar with the matter has told Reuters.
Stadler's arrest is the most high-profile yet in the diesel gate crisis, which started when the Volkswagen group admitted in 2015 to equipping some 11 million diesels worldwide with "defeat devices" created to dupe pollution tests. The company has earmarked more than €27bn in fines, buybacks and costs.