The bill, which had sparked days of protests, would have allowed businesses to deny service to gay and lesbian customers based on religious beliefs.
Governor Brewer said the bill could have created more problems than it was attempting to solve.
"The bill is broadly worded and could result in unintended and negative consequences," Governor Brewer said.
Supporters argued the bill was not about discrimination.
"People want to be able to have their belief systems respected," said Maia Arneson with Arizona's Christian Business Networking.
Arizona currently has a ban on gay marriage.