Audi and VW confirmed the arrest and reiterated there was still a presumption of innocence for Stadler.
Stadler's arrest is the most high-profile in the diesel emissions scandal.
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.
The Volkswagen emissions scandal began in September 2015, when the United States Environmental Protection Agency (EPA) issued a notice of violation of the Clean Air Act to German automaker Volkswagen Group. "The suspect has been seen by a judge, who has ordered him to be remanded in custody", the prosecutors' office said in a statement. Munich prosecutors and Stadler himself were not immediately available for comment.
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"His arrest is another low point in VW's diesel saga", said Evercore ISI analysts, who have criticized the company for being slow to reform.
Prosecutors said the arrest was justified because of the "risk of concealment of evidence". The executive was arrested at his home in Ingolstadt in the early hours on Monday, they said. Until now, backing of the Porsche and Piech families, who control the world's biggest auto maker, ensured him continuing in the role he's held since 2007.
At 1040 GMT, VW shares were down 2.7 per cent at 156.70 euros, one of the biggest falls by a European blue-chip stock. Before becoming Audi CEO in 2007, Stadler worked as chief of staff to VW's former chairman Ferdinand Piech.
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. The company has earmarked more than €27 billion in fines, buybacks and costs.