VW's luxury subsidiary Audi has long faced suspicions that its engineers developed the software used in the scam. However both USA and German authorities have arreested several engineers including Porsche engine and development chief Wolfgang Hatz.
The move is an extension of the emissions scandal that has rocked Volkswagen since 2015 and led to billions in fines, the arrest of executives and the indictment in the USA of its former CEO.
Last month, Audi admitted that another 60,000 A6 and A7 models with diesel engines have emission software issues.
Auto industry expert Ferdinand Dudenhoeffer of the vehicle research centre called the allegations against Stadler "very serious".
News of the arrest comes as VW's new group CEO Herbert Diess is trying to introduce a new leadership structure - which includes Stadler - and speed up the group's shift towards electric vehicles in the wake of the biggest motoring scandal in modern history. Volkswagen's supervisory board has been scheduled to meet on the same day; the board is expected to discuss the diesel investigation and Stadler's arrest.
Prosecutors pushed for Stadler's arrest over fears that he might try to evade justice, dpa reported.
Volkswagen has pleaded guilty to the criminal charges pressed against the company where two managers are serving prison time in US.
They are suspected of knowing earlier than they have admitted about the cheating, meaning they may have failed in their duty to inform investors in the auto giant about the financial risks.
U.S. prosecutors also indicted Winterkorn last month, saying he knew of the company's emissions cheating as early as May 2014 but made a decision to continue.
Stadler is the most senior company official so far to be taken into custody over the German carmaker's part in the emissions cheating actions first highlighted in 2015. That has cost it $20 billion in fines and civil settlements.
In doing so, VW said it admitted its "responsibility for the diesel crisis". Prosecutors said last week they had searched Stadler's home for evidence as part of an investigation that has been underway for over a year. He was charged with wire fraud and conspiracy to defraud American customers and violate the Clean Air Act.
VW engineer James Liang, who cooperated with investigators, was handed 40 months in jail past year.