Kindervater is retiring from the group at the end of the year to work as a freelance PR consultant.
It is not known whether Kindervater will be replaced.
A Deutsche Telekom sp-okesman said the appointment this week of its new CEO Kai-Uwe Ricke will see a review of the company's strategy, including communications.
He added that the review will look at the global communications role and whether a direct successor is needed.
Kindervater has headed press relations, corporate identity and advertising for the group since 1991.
V-P of corporate communications Ulrich Lissek continues to lead global corporate communications.