The 56-year-old auditor and tax consultant worked for the Edeka Group for over 30 years.
The company added that Rainer Huber will take over the departments of controlling, finance and accounting, real estate, IT, human resources and law, which Wilkens has been responsible for in recent years.
"We very much regret Ms. Wilkens' decision, but we respect it," said Uwe Kohler, chairman of the Edeka Südwest board of trustees.
"We would like to thank her for what she has achieved and for the very good co-operation and wish her all the best for the future."
Edeka Südwest has around 1,120 stores, six logistics centres and six production facilities in five federal states across Germany. This makes it the second largest of the seven regional companies in the Edeka Group.
With more than 44,000 employees and around 3,000 trainees in over 30 apprenticeships and dual courses of study (all figures including independent retail), Edeka Südwest is one of the largest employers and training companies in the region.
In December, Edeka Südwest launched a human resources development project, 'Fit for intern support', in which students and trainees are prepared to support interns in the company.
Phanthipha Chiamchamratrot, training supervisor at Edeka Südwest, developed the concept along with her colleagues from the training team and is now implementing it.