Management guru Jeffrey Sonnenfeld on Friday called for a leadership shake up at Facebook, slamming COO Sheryl Sandberg after her denial of a New York Times report that she ignored Russian activity on the social network and thwarted investigations.

Sandberg should "probably should be replaced," said Sonnenfeld, senior associate dean for leadership studies at Yale University. She's "completely dispensable," he said on CNBC's "Squawk Box," adding that she should at least be put on probation.

Meanwhile, Facebook's Mark Zuckerberg should no longer be chairman, Sonnenfeld argued, saying the co-founder should focus on being just the CEO and to "perform a lot of the great fixes" to the brand.

Someone like board member Erskine Bowles — a longtime anti-debt crusader in Washington and also White House chief of staff under former President Bill Clinton — should be made chairman, Sonnenfeld said. He went on to say that Facebook should also return former Washington Post publisher Don Graham to the company's board. Graham was a "great mentor to Mark Zuckerberg when he was hiding under the hoodie."

New York City Comptroller Scott Stringer, appearing later Friday morning on "Squawk Alley," said the Times' expose was "damaging" and "confirmed our worse nightmare."

Criticizing the company's structure, he also said the best practice would be to install a new chairman. "You separate the chair from the CEO. They're two different responsibilities," he argued. "Someone has to oversee the work of Mr. Zuckerberg and Ms. Sandberg."

The comptroller's office overseas New York City's $195 billion pension program that includes 4.5 million shares of the social media firm. At around $138 per share, that's about a $620 million stake.

"Our job is not to get out of companies. Our job is to stay and make sure these companies create the greater return" for teachers, police officers, firefighters, and other people on the city's public pension fund, Stringer said.

Shares of Facebook were under intense pressure Friday — down about 36 percent from their 52-week highs in July.

Facebook didn't immediately respond to CNBC's request for comment.