"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. Stadler was under investigation for malpractice in the emissions cheating scandal at Volkswagen.
Martens led a diesel task force at Audi, set up to coordinate the handling of the so-called Dieselgate scandal with its parent company.
Two former VW chief executives - Martin Winterkorn and his successor Matthias Mueller - have both landed in the sights of German prosecutors. Stadler, 55, has been placed on leave after Munich prosecutors took him into custody in the early hours at his home in Ingolstadt, Germany, they said.
"We confirm that Mr. Stadler was arrested this morning".
Audi has not yet commented on the matter.
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.More news: Beyonce and JAY-Z Release Surprise 'Everything is Love' Album on Stage
It was in September 2015 when VW admitted to using illegal software to cheat US emissions tests on diesel engines.
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.
The Munich prosecutor's office is reportedly working towards the investigation of 19 other suspects, identities of whom haven't been disclosed, yet.
The scandal has so far cost the VW group more than 25 billion euros ($29 billion) in buybacks, fines and compensation, and the company remains mired in legal woes at home and overseas.
A judge has ordered him to remain in detention on suspicion that he may supress evidence or collude with fellow executives that are due to meet at a Volkswagen Group Supervisory Board meeting later this week, where lawyers were expected to present information in defence of 20 senior VW Group employees now under investigation.
But investigations are continuing elsewhere.
Volkswagen, which last week agreed to pay a fine of €1 billion ($1.2 billion) imposed by German prosecutors, confirmed the arrest.