Christopher Ailman, the chief investment officer of the California State Teachers' Retirement System (CalSTRS), said Wednesday he deleted his Facebook account because of the company's management.

In a tweet, he said: "I have deactivated my Facebook account. Their lack of oversight and poor management is offensive. #DeleteFacebook."

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CalSTRS, which manages $224.4 billion in assets, owns $650.4 million in Facebook shares as of year-end 2017.

Ailman's tweet comes as Facebook struggles with the news that Cambridge Analytica, a political analytics firm, was able to collect data on millions of people's profiles without their consent. The news was followed by a steep decline in the company's stock and raised concern it could be hit with government regulation.

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

In an interview with CNBC on Wednesday, Ailman said: "They have to deal better with their privacy issues. We've been unhappy about the governance [in Facebook] because as shareholders we have almost no say, because [CEO Mark] Zuckerberg just controls that thing."

"While Silicon Valley loves to have one person in charge, we think there are drawbacks," he said.

Facebook's stock 2.7 percent on Thursday after Zuckerberg told reporters he has not seen a noticeable change in user behavior amid the scandal. Zuckerberg is scheduled to testify in front of Congress on April 11.