"I thought it was one of the most devastating stories I've read," said Cramer, who has recently been critical of Sandberg and whose charitable trust owns shares of Facebook. "This was distinctly ill-advised. How does this person stay there? How does she stay?"
According to the Times report, Sandberg told subordinates in January to carry out research on the financial interests of hedge fund billionaire George Soros, who had criticized the company during a speech at the World Economic Forum in Davos, Switzerland, that same month.
Sandberg was reportedly attempting to gauge whether Soros stood to gain financially from the attacks by shorting Facebook's shares, a practice in which traders can bet against a company by selling shares they don't own and buying them back at a lower price.
But in response to the Times report, a Facebook spokesperson told CNBC that the company researched possible motivations behind Soros' criticism of the company before Sandberg inquired about Soros. Facebook's stock was up nearly 1 percent in midmorning trade Friday after the report.
Cramer said last week that Facebook's stock could rise if Sandberg resigned or was ousted. His remarks followed a Wall Street Journal report, which said Facebook CEO Mark Zuckerberg placed blame on Sandberg for the company's problems, including its Cambridge Analytica scandal and subsequent public disclosures.
The "Mad Money" host on Friday reiterated his argument that Facebook should hire an outside counsel to investigate the company's recent scandals and "let the chips fall."
"That's what they should do. They're in their own world," Cramer said on "Squawk Box." He later said, "I find Facebook to be rogue" after reading the Times report.
Facebook declined to comment on Cramer's remarks.