Senate bill 1062 would have given business owners the legal right to refuse service to anyone if doing so would conflict with “sincerely held” religious views.
Brewer, a Republican, said she was unconvinced the bill addressed an issue of religious liberty in Arizona and argued its broadly-defined powers could have “unintended and negative consequences”.
“To the supporters of the legislation, I want you to know that I understand that long-held norms about marriage and family are being challenged as never before,” Brewer said in a statement.
“Our society is undergoing many dramatic changes. However, I sincerely believe that Senate Bill 1062 has the potential to create more problems than it purports to solve. It could divide Arizona in ways we cannot even imagine and no one would ever want.”
Since the bill was passed by the Republican-controlled Arizona state Senate last week it has attracted criticism from across the US, with many arguing it would have allowed businesses to deny service to anyone from gay men to unmarried mothers.
Several major companies including Apple and American Airlines argued the law would damage the state’s economy. Prominent Republicans including John McCain and Mitt Romney also called for a veto and in the face of national criticism a number of Arizona Senators who signed the bill publicly recanted their positions and said they would argue for a repeal of the law if it passed.