BERLIN—The chief executive of Volkswagen AG’s luxury unit Audi was jailed Monday without bail after prosecutors said they were worried he might try to interfere in a probe into whether he was involved in the German car maker’s diesel-emissions cheating scandal.

The arrest of the executive, Rupert Stadler, came a week after Munich prosecutors searched his home and said they had added him to a list of about 20 suspects in a broad fraud investigation stemming from the scandal.

Volkswagen...