Munich prosecutors, who earlier this month widened their probe into Audi, said Rupert Stadler was being held due to fears he might hinder their investigation into the scandal, plunging Volkswagen into a leadership crisis.
In the Reuters report, Stadler had his contract extended in 2017 and was named as a suspect alongside another unnamed member of Audi's board of management.
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.
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".
Even though buybacks and fixes are in full swing around the world, the fallout from Volkswagen's diesel scandal continues with a high-profile arrest.
Audi has not yet commented on the matter.
Volkwagen Group was accused of selling diesel cars with software that turned on full pollution controls only when the vehicle was undergoing official emissions testing. The 55-year-old was arrested at his home in Ingolstadt in the early hours on Monday, they said.
VW has pleaded guilty to criminal charges in the United States. Herbert Diess was given the top job in April and he said that besides focusing on new technologies, like electric cars, he wanted to build a more open, values-based culture to avoid the cheating that led to the emissions scandal.
Diesel cars from Volkswagen and its Audi subsidiary cheated on clean air rules with software that made emissions look less toxic than they actually were.
Volkswagen, which last week agreed to pay a fine of €1 billion ($1.2 billion) imposed by German prosecutors, confirmed the arrest.