Martin Winterkorn, the former boss of Volkswagen who quit last month, will step down from his remaining posts related to the company.
The Gulf region has become a leading market for luxury cars and wealthy individuals are set to buy a record number of vehicles from the likes of BMW's Rolls-Royce, Fiat's Maserati and Porsche SE this year.
Volkswagen did not name a successor, but said proposals on management appointments would be made to a full board meeting on Friday.
Late on Monday, Volkswagen's U.S. chief Michael Horn said the company had "totally screwed up" and promised to make amends.
It was in the 1960s that the Beetle attained its cult status, when it became almost synonymous with the hippie movement -- and succeeded in shaking off the grim history of its origins. As Volkswagen announces the end of the Bug's journey, Amrita Singh goes down a nostalgic road.