GE on Monday said its chairman and CEO, 61-year-old Jeff Immelt, is stepping down after 16 years. John Flannery, 55 — current head of GE Healthcare — takes over as chief executive Aug. 1 and then adds the chairman title when Immelt officially retires Dec. 31.
"Someone who was with [Flannery] all weekend was very adamant to me that the idea that he has a plan to break the company up you just take that narrative off the table," Cramer said on "Squawk on the Street." "As soon as you start talking about a sum of the parts, a breakup, you're talking about the dividend being in jeopardy."
CNBC's David Faber, who specializes in mergers and acquisitions, said he was also hearing the same thing as Cramer: "Nobody is expecting [Flannery] to break it up."
In a statement emailed to CNBC, GE said: "Break-up shouldn't be part of the discussion. Over the next few months, John will perform a focused review on all aspects of the company. We will continue to take actions that deliver value to GE shareowners. John will focus ... on execution and accountability, both internally and externally, short-term and long-term."
Since Immelt became CEO in 2001, GE's shares have fallen 30 percent, while the S&P 500 has more than doubled. That underperformance had some pressing for more urgency from Immelt who's led a transformation at GE to focus on its core industrial businesses and selling off units, including the divestiture of GE Capital's operations.
Activist investor Nelson Peltz's Trian Fund, which owned 68.9 million shares of GE worth $2 billion as of March 30, has criticized the company's performance and pressed for asset sales and cost-cutting. Trian said it has "no comment" on the leadership change.
"I do have behind the scenes on Flannery, the new CEO, which he is a seemingly jovial man who's not. I'm getting that from a couple people," said Cramer, who said Immelt is "jovial" and was more of "an ambassador of good will" for the company.
— Reuters contributed to this report.