Before becoming Audi CEO in 2007, Stadler worked as chief of staff to VW's former chairman Ferdinand Piech.
Audi has been caught up in the diesel emissions scandal that has plagued VW.
While it has been confirmed that he has been arrested, no other details about his prosecution are available at the moment. Stadler has denied any involvement.
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. The luxury carmaker is also being investigated for allegations of fraud and illegal product promotion.
"We confirm that Rupert Stadler was taken into custody pending trial this morning at the request of the Munich II Public Prosecutor's Office", an Audi spokesman tells NPR.
Stadler is being held because the police are concerned that he might obstruct the investigation into Audi's diesel vehicles. The 55-year-old was arrested at his home in Ingolstadt in the early hours on Monday, they said.
Martens led a diesel task force at Audi, set up to coordinate the handling of the so-called Dieselgate scandal with its parent company.
Martin Winterkorn, the former chief executive officer of Volkswagen, was indicted in May by United States prosecutors. It said shortly afterward that a judge had ordered him kept in custody pending possible charges at prosecutors' request.
A spokesperson for Porsche SE, which controls VW and Audi, said Stadler's arrest would be discussed at a supervisory board meeting on Monday.
Munich prosecutors searched Stadler's private residence as part of their investigation of suspected fraud and indirect improprieties with documents. "The presumption of innocence continues to apply for Mr. Stadler". The 56-year-old executive was named to Audi's management board last year, long after the scandal erupted.
But investigations are continuing elsewhere.
Just last week, VW agreed to pay a one-billion-euro fine to settle a probe by German prosecutors.
Fed Raises Interest Rates, Signals 2 More Hikes This Year
And their rate increases are addressing the "perceived threat of inflation", not an immediate inflation problem, he said. Still to come in the economic calendar are Germany and France inflation readings at 0700 BST and 0745 BST respectively.