The measure sought to split the CEO and chairman roles and install an independent chair. Zuckerberg serves both as CEO and chairman, as well as controlling a majority of voting shares.
Capping off a difficult year marred by numerous leaks and scandals, shareholders supporting the proposal argued that the move is necessary to ensure that there are proper checks on Zuckerberg's power.
The proposal been expected to fail because of Zuckerberg's control of voting shares.
Nonetheless, Trillium Asset Management, one of the proposal's backers, said in a statement that should it receive more than 30% of votes, the results will "send a strong message to Mark Zuckerberg and the board that main street and Wall Street investors are seeking an independent board chair."
The final tally will be counted next week. Facebook shares were roughly flat on Thursday. They are up 34% so far this year.