On Wednesday evening, the board made some changes to the ban before passing it by a vote of 3-2.
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One change was aimed at convincing the College Board to keep its Advance Placement designation on some courses, even if certain topics are not allowed to be discussed.
The ban does not specify what would happen if a teacher were to violate the policy.
The district is the first in Orange County to pass such a rule.
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Critical race theory is a way of thinking about America's history through the lens of racism. Scholars developed it during the 1970s and 1980s in response to what they viewed as a lack of racial progress following the civil rights legislation of the 1960s.
It centers on the idea that racism is systemic in the nation's institutions and that they function to maintain the dominance of white people in society.
The architects of the theory argue that the United States was founded on the theft of land and labor and that federal law has preserved the unequal treatment of people on the basis of race. Proponents also believe race is culturally invented, not biological.
Many Republicans view the concepts underlying critical race theory as an effort to rewrite American history and convince white people that they are inherently racist and should feel guilty because of their advantages.
But the theory also has become somewhat of a catchall phrase to describe racial concepts some conservatives find objectionable, such as white privilege, systemic inequality and inherent bias.
The Associated Press contributed to this report.