HPE shares were down 8 percent.
HPE's president, Antonio Neri, will succeed Whitman on Feb. 1, the company said Tuesday.
"Antonio's ready, the company's ready, and it's the right time," Whitman said in an interview Wednesday on CNBC's "Squawk on the Street."
"I've said for many years the next CEO of this company needs to be someone we have promoted from within, someone who is a deep enterprise technologist, who knows the company — loves the company."
Whitman, who ran unsuccessfully for governor of California in 2010 as a Republican and endorsed Hillary Clinton in the 2016 presidential election, told CNBC she would "definitely not be running for office."
Whitman joined Hewlett-Packard in 2011 and oversaw the company's split into two brands. She remained as CEO at the newly streamlined HPE, prioritizing cloud services and spinning off product and consumer hardware to HP Inc.
Whitman is leaving a decidedly different company than the one she joined six years ago, having pushed for the company's split.
"I believe the future belongs to the fast," Whitman said. "And it was just too big and too cumbersome and competed in too many markets to do the very best job in all of them."
Her tenure at HPE saw a ramping up of acquisitions — eight in the last two years, she told CNBC.
Neri has been with the company since 1995, working his way up to the company's top ranks. Whitman will remain on the board and Neri will join it, the company said.
"[Neri] and I have been joined at the hip in deciding about those acquisitions," Whitman said. "He's been really my right-hand executive for well over four years."
Whitman said she is not sure of her next step, but that any next CEO position would have to be "exactly the right opportunity."
She reportedly spoke to Uber about a CEO position after the ride-hailing company booted founder Travis Kalanick in June. The company selected Dara Khosrowshahi.
Whitman told analysts Tuesday that she'll be taking a little downtime and said there's "no chance" she will join a competitor to HPE or HP.
Whitman said she is concerned that her departure means one less female CEO.
"I think in the last couple of decades, we made a lot of progress in the number of CEOs and number of female executives in the C-suite. It has stalled out in the last decade, if you look at the data, and I think that's concerning," she said.
— CNBC's Anita Balakrishnan and Jordan Novet contributed to this report.