The arrest comes as Volkswagen seeks to settle criminal allegations stemming from its admission in 2015 that it rigged nearly 600,000 diesel-powered cars sold in the U.S. to cheat on emissions tests. Volkswagen has agreed to pay up to $17.5 billion in the U.S. to settle claims with regulators, consumers, dealers and state attorneys general and could face another multibillion-dollar penalty in the expected criminal case.

Volkswagen declined to comment. The executive, Oliver Schmidt, couldn't be reached via email or his mobile phone for comment.

The news of Mr. Schmidt's arrest was reported earlier by the New York Times.

Mr. Schmidt served as head of Volkswagen Group of America's Engineering and Environmental Office in Ann Arbor, Mich., from 2014 to early 2015. He is still an employee of Volkswagen, based in Wolfsburg, Germany.