The 55-year-old German is being held due to the risk that he could prevent evidence from being found, the prosecutor's office has said.
In a statement to USA Today, Audi said it has no further comment to make on the matter, adding that the presumption of innocence continues to apply for Stadler. "The hearing to determine whether he will be remanded is ongoing". At the end of May, authorities named Stadler and Audi board member Bernd Martens as two key suspects among 18 being investigated in the emissions investigation.
Munich prosecutors said Mr Stadler would be questioned by Wednesday, once he had spoken to his lawyers.
Stadler, the former chief of staff to VW's powerful former chairman Ferdinand Piech, had been handed the post as head of Audi in an effort to promote the automaker's transition to electric-car production.
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The stock fell as much as 4.1 percent, its biggest intraday drop since February.
Last month, it admitted that another 60,000 A6 and A7 models with diesel engines have emission software issues.
VW has so far set aside around $30 billion to cover the cost of fines, vehicle refits and lawsuits related to its emissions test cheating.
Volkswagen has admitted using special software to cheat on emissions tests, with almost 11 million vehicles affected. He was charged with wire fraud and conspiracy to defraud American customers and violate the Clean Air Act. The German government a year ago accused Audi of cheating on its emissions tests for high-end models.
It is worth mentioning here that Volkswagen's luxury auto brand Audi has earlier faced suspicions that its engineers had developed a software used in the diesel emission scam.