By any standard, Rupert Stadler, the chief executive of Volkswagen’s Audi luxury car division, is a survivor.

When evidence emerged that Audi had played a major role in developing illegal emissions software on Mr. Stadler’s watch, he and most other top executives kept their jobs. When an outside monitor faulted Volkswagen for failing to hold executives accountable, Mr. Stadler stayed in place. And when Munich prosecutors identified him last week as a suspect in their investigation and searched his home for evidence, Volkswagen said its management board had not even discussed his dismissal.

That run may well be ending, however. On Monday, German authorities arrested Mr. Stadler, 55, holding him indefinitely pending trial, an acute embarrassment for Volkswagen — and one that could finally prod the company to action.

Mr. Stadler’s arrest is the latest example of German officials widening their investigation into diesel cheating at Volkswagen. The company was found in 2015 to be using software to artificially lower a vehicle’s emissions levels when it was undergoing tests. So far, the inquiry into the scandal has largely been led by authorities in the United States, where the carmaker has had to pay tens of billions of dollars in fines and settlements, and where several executives have been arrested or sentenced to jail.