Walden, the company's top-ranking female executive, played a big role in Verizon's acquisition of Yahoo and its merger with AOL to create the Oath unit.
Walden, who was seen as a potential successor to Chief Executive Lowell McAdam, will move into a strategic adviser role from Dec. 31, until her departure.
"She is leaving because she wants to pursue other opportunities. This is not related at all to yesterday's news," said a company official, speaking on condition of anonymity.
Yahoo said on Tuesday that all 3 billion of its user accounts were hacked in a 2013 data theft, tripling its earlier estimate of the size of the largest breach in history.
Walden most recently spearheaded Verizon's entry into global digital media and telematics, the company said.
Oath CEO Tim Armstrong will report to McAdam after Dec. 31, while the telematics organization will report to John Stratton, executive vice president and president of Verizon's Global Operations, Verizon said.
"Marni helped build our wireless business, starting as a sales representative in a store, and grew into an inspirational leader and role model for so many at Verizon," McAdam said.
(Reporting by Munsif Vengattil in Bengaluru and David Shepardson in Washington; Editing by Martina D'Couto and Anil D'Silva)