"The company is not well managed," said Brian Wieser, a senior research analyst at Pivotal Research Group with a sell rating on Facebook's stock. He's one of two analysts with a sell rating, according to FactSet. "One of Zuckerberg or Sandberg will not be in the same jobs in 12 months time."
The social media giant came under fire over its privacy practices in the wake of revelations that Cambridge Analytica improperly gained access to data from some 87 million user profiles, then used it to target political ads.
It's important to note, a Zuckerberg resignation would be unlikely as the co-founder, CEO and chairman is the controlling shareholder of the company.
Shortly after the revelation of the data scandal, there was some speculation as to whether Facebook's board would ask Zuckerberg to step down from his current role. Zuckerberg quickly dismissed those rumors, saying he is not aware of any board discussions and that he's the "best person to run the company." He also said no has been be fired as a result of the data leak. As for Sandberg, Zuckerberg has praised her repeatedly.
Wieser said Tuesday, however, there are systemic problems with Facebook, including how it handles data and content. "I don't think investors fully appreciate that risk," he told "Squawk Box." "This is not the last time we're going to see problems from them." CNBC has reached out to Facebook for comment about Wieser's comment.
Zuckerberg will begin two days of Capitol Hill testimony over the social network's privacy practices on Tuesday.
Ronald Josey, managing director of equity research JMP Securities, told CNBC that Zuckerberg has done a good job at handling the aftermath of the data scandal. He said that over the next few months there will be a headline risk on the social network's stock.
"When we look out for the next several years at Facebook and we think about the number of users ... we think they can actually manage through this," Josey, who has an outperform rating on Facebook, told "Squawk Box."