Tucson school officials have insisted the program only aims to provide students with courses about the role of minorities in historical events such as the Vietnam war or literature courses featuring Latino authors.
The bill signed by Brewer on Tuesday prohibits any classes which promote the overthrow of the United States government, promote resentment toward a race or class of people, or are tailored for pupils from a particular racial group.
The law was approved by Brewer despite condemnation from a panel of United Nations human rights experts released several hours earlier.
In a lengthy statement condemning Arizona's immigration law, the experts said the education bill was at odds with "the right of everyone to have access to his or her own cultural and linguistic heritage."
"Everyone has the right to seek and develop cultural knowledge and to know and understand his or her own culture and that of others through education and information," the UN panel said.
Brewer attracted outrage after approving an immigration law last month which makes it a crime in Arizona to lack proper immigration papers and requires police to determine whether people are in the country illegally.
Civil rights activists say the law will open the door to racial profiling by law enforcement officers. Supporters of the law say the bill expressly forbids police from stopping someone on the basis of their ethnicity.
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