The shareholder proposal follows a series of controversies and scandals at the technology firm, including large-scale data breaches and accusations that the social network has become a platform for misinformation campaigns and political propaganda.
State and city treasurers from Illinois, Rhode Island and Pennsylvania joined the New York City Pension Funds and Trillium Asset Management in requesting the Facebook board of directors to make the role of chairman an independent position.
"Doing so is best governance practice that will be in the interest of shareholders, employees, users, and our democracy," the filing states.
The proposal cites Facebook's "mishandling" of "severe controversies," including how the social network was used to manipulate the 2016 US presidential elections through Russian troll farms, and the sharing of data with Chinese device manufacturers like Huawei.
According to the shareholders, Facebook's governance structure puts investors at risk and should fall in line with other major tech firms like Google, Microsoft and Apple in having separate CEO and chairperson roles.
"Facebook plays an outsized role in our society and our economy. They have a social and financial responsibility to be transparent – that's why we're demanding independence and accountability in the company's boardroom," said New York City Comnptroller Scott Stringer.
"An independent board chair is essential to moving Facebook forward from this mess, and to reestablish trust with Americans and investors alike."
The proposal will be put to a vote at the company's annual shareholder meeting in May 2019, however it will be largely symbolic due to the control that Mr Zuckerberg has over the company's board.
Mr Zuckerberg's reign at Facebook has previously been compared to a dictatorship because he owns a majority of voting rights to the firm.
In an op-ed earlier this year, a member of the California State Teachers' Retirement System (CalSTRS), which holds shares in Facebook, called for the company to make changes to reflect its size.
"Facebook has grown at an unbelievable pace. The capital structure has changed and it is time for its governance to catch up," CalSTRS investment officer Aeisha Mastagni wrote in The Financial Times.
"Why does Mr Zuckerberg need [voting control]? Is it because he does not want governance to evolve with the rest of his company? If so, this American dream is now akin to a dictatorship."
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