Facebook's response to its recent data breaches is like playing a game of "whack-a-mole" instead of addressing the root issues with its business model head-on, Elevation Partners co-founder Roger McNamee told CNBC on Monday.

The social network is "attacking individual problems as though they're isolated and unrelated to everything else," argued McNamee, an early Facebook investor and frequent critic. "That is never going to work."

Facebook came under fire once again for its data security practices on Monday when the Japanese government issued a statement pressuring the company to better protect users' personal data.

Last month, Facebook revealed that an attack on its network had exposed the data of 50 million users, the largest breach in company history. At the same time, the company is still reeling from the Cambridge Analytica scandal earlier in the year, when it was discovered that the political consulting firm, which worked on President Donald Trump's campaign, had harvested data from up to 87 million profiles.

Without systemic change at the company, McNamee believes these problems will only continue. "Every time you turn over a rock, there's going to be something ugly under it," he said in an interview with "Squawk Alley."

"The problem is that Facebook has a systemic issue in the way its algorithms and business model work," McNamee said, reiterating his belief that Facebook's ad-based business model is inherently at odds with the need to protect user data.

"In order for this problem to go away, the business has to earn less money," offered McNamee, saying that investors might then push for changes.

Facebook shares tanked in July after the company warned investors of a revenue slowdown later in the year, partially caused by more investment into data protection. The stock is down about 11 percent this year.

With regards to the growing calls on co-founder Mark Zuckerberg to split his two roles of CEO and chairman, McNamee is unconvinced that the change would have much of an impact.

"You're not going to fix this with corporate governance. You have to change the product. You have to change the business model," he said.

Similarly, McNamee believes Facebook's potential acquisition of a cybersecurity firm, as reported over the weekend by The Information, is "not going to solve the problems."

Facebook did not immediately respond to CNBC's request for comment.