The unexpected departure comes after Bild am Sonntag newspaper last week reported that an internal investigation by US law firm Jones Day had found that Knirsch knew that Audi's 3.0-litre diesel engines were equipped with cheating software before the scandal erupted.
The sophisticated software could detect when the cars were undergoing regulatory tests and lower their emissions accordingly to make them seem less polluting than they were.
Audi declined to comment further when contacted by AFP. The company did not say in its statement who would replace Knirsch. The VW group, which has announced a mass recall to repair the affected vehicles, has had to set aside billions to cover costs and fines over the scandal.
Its share price remains more than 20%t lower than it was before the crisis broke. On Monday, VW shares closed 2.6% lower in Frankfurt, underperforming the DAX 30 index which fell by 2.3%.