The move follows a search last week of Stadler's private residence, ordered by Munich prosecutors investigating the manager on suspicion of fraud and indirect improprieties with documents.
The Dieselgate scandal dates back to 2015, when Volkswagen was caught out by US authorities for installing emissions cheating defeat device software in millions of diesel vehicles sold worldwide.
Last week, the prosecutors' office widened its emissions cheating probe to include Stadler among the suspects accused of fraud and false advertising.
"The presumption of innocence remains in place for Mr. Stadler", Audi said.
The Munich prosecutor's office is reportedly working towards the investigation of 19 other suspects, identities of whom haven't been disclosed, yet.
"Audi CEO Rupert Stadler was provisionally arrested this morning", Audi said in a statement.
Audi had no immediate comment.
The fallout has cost VW more than $30bn to date - the bulk of that sum in the U.S. where, in May, prosecutors filed criminal charges against former VW boss Martin Winterkorn. Munich prosecutors told the state-owned broadcaster that they swooped on Stadler over fears he might try to suppress evidence in the ongoing Dieselgate investigation. The executive was arrested at his home in Ingolstadt, in the early hours on Monday, they said.