Stadler, 55, who joined Audi in 1990 and has been its CEO since 2007, has enjoyed the full backing of VW's top brass so far. German automaker and Audi's parent company Volkswagen confirmed the detention.
Volkswagen first admitted in 2015 it had rigged millions of diesel engines to cheat on emissions tests.
Four police officers detained the Audi boss at his home at between 6 and 7 am, a spokesman for Munich prosecutors told AFP, saying that the arrest was justified as he is suspected of "seeking to influence witnesses or other suspects". Stadler has denied any involvement.
In November 2015 Audi admitted installing emissions defeat devices in its cars, and Audi's been pegged in several reports as the source of the initial defeat software responsible for Dieselgate. The luxury carmaker is also being investigated for allegations of fraud and illegal product promotion.
Stadler was arrested after a warrant was issued by a Munich prosecutor, the Sueddeutsche Zeitung newspaper reported, adding that his personal flat had been searched by fraud investigators last week.
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Audi had no immediate comment.
The executive was arrested at his home in Ingolstadt in the early hours on Monday, they said.
Rupert Stadler, CEO of German auto producer Audi, briefs the media during the annual press conference in Ingolstadt, Germany.
Volkswagen has pleaded guilty to criminal charges in the United States and nine managers, including former CEO Martin Winterkorn, were charged there.
"We confirm that Mr. Stadler was arrested this morning". However, the Audi spokesperson suggested that in this case, the presumption of innocence continues to apply. He was named a suspect by the Munich prosecutor's office alongside an unnamed member of Audi's board of management. Speaking of the entire group, it was only last week when VAG received a hefty €1 billion ($1.18B) fine linked to the diesel emissions debacle, one of the many fines the German automotive conglomerate has received in recent times because of the Dieselgate.