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.
Stadler is the most senior company official to be detained so far since Volkswagen (VW) admitted in September 2015 to using illegal software to rig USA emissions tests on diesel engines.
Prosecutors pushed for Stadler's arrest over fears that he might try to evade justice, dpa reported.
Munich prosecutors had conducted searches at Stadler's private residence as a part of the probe concerning alleged fraud and indirect improprieties with documents. VW's representative went on to mention the presumption of innocence has been applied.
The agency found that Volkswagen had intentionally programmed turbocharged direct injection (TDI) diesel engines to activate their emissions controls only during laboratory emissions testing which caused the vehicles' NOx (Nitrogen Oxides) output to meet U.S. standards during regulatory testing, but emit up to 40 times more NOx in real-world driving.
The auto manufacturer pleaded guilty to criminal charges in the United States and nine managers, including former CEO Martin Winterkorn, were charged. Volkswagen's supervisory board is meeting today, where Stadler's future will be among the topics of discussion.
Just last week, Volkswagen agreed to pay a 1 billion-euro fine imposed by German prosecutors for cheating to get around diesel-emissions regulations.
Most of its problems have been in the United States, where a total of nine people have been charged and two former VW executives have pleaded guilty and been sentenced to prison terms.
"Audi needs a new start", he said.
Volkswagen declined 2.2 percent to 157.88 euros and traded 2 percent lower at 11:50 a.m.in local trading, extending losses this year to 5.2 percent.