Ms Brewer said the bill could have had "unintended and negative consequences".
It was touted as a religious liberty protection by social conservatives. Its opponents denounced it as legalising anti-gay discrimination.
Business groups warned it would tarnish the state's reputation and discourage companies from moving to the state.
'Creates problems'Analysis
The broad-reaching bill was based around protecting religious freedoms, but would also have given legal protection to those discriminating against others.
Its authors argued people should be allowed not to sell something or serve someone, if doing so went against their religious beliefs.
Its opponents were big and powerful - the gay rights movement in America has momentum and strong support.
Apple, which is bringing a new factory and 2,000 jobs to Arizona, urged the governor to veto the bill, as did American Airlines, the Marriott hotel chain and the group responsible for bringing the next Super Bowl to the state.
The leader of the Chamber of Commerce said a huge majority of businesses opposed the bill, and for a pro-business governor trying to pull the state out of recession this was a persuasive argument.
Local Republican Senator John McCain and former presidential candidate Mitt Romney all pressed for a veto. Governor Brewer had held private briefings with opponents, and religious conservatives who proposed the bill all day before announcing her decision.
Speaking to reporters on Wednesday afternoon, Ms Brewer, a Republican, said the bill did "not address a specific or present concern related to religious liberty in Arizona".
"I have not heard one example in Arizona where a business owner's religious liberty has been violated," she said of the bill, which passed the state legislature last week with the strong backing of the state's Republican Party.
Ms Brewer spent Wednesday huddling with both supporters and opponents of the bill and said she had vetoed it because she believed it had "the potential to create more problems that it purports to solve".
"It could divide Arizona in ways we cannot even imagine and nobody could ever want," she said.
In doing so, Ms Brewer sided with the business community - including firms such as Intel, Yelp, Marriott and Major League Baseball and the Arizona Chamber of Commerce.
Loud cheers erupted outside the Arizona capitol building immediately after the governor announced the veto.
Rebecca Wininger, president of Equality Arizona, told the BBC the veto was "a clear message for those trying to use religion and those with right-leaning rhetoric that we're done... we're tired and we're done with being discriminated against".
Even as the federal government, the military, the courts, other states and US public opinion increasingly back gay rights and same-sex marriage, some states have seen the makings of a backlash in recent weeks, analysts say.
"Religious liberty" bills similar to the Arizona measure have been introduced in seven other US states, but Arizona's was the only legislature to send a bill to the governor.
'Distorted the bill'The bill would have expanded the state's religious liberty law to add protection from lawsuits for individuals or businesses that cited their "sincerely held" religious beliefs as motivating factors in taking an action or refusing to do so.
Supporters cheered outside the state Capitol on Wednesday after Ms Brewer announced her vetoAll but three Republicans in the state legislature voted for the proposal, known as SB1062, but some Republican state senators who voted for the bill subsequently called for a veto.
"We were uncomfortable with it to start with and went along with it thinking it was good for the caucus," Senator Steve Pierce told the Associated Press news agency on Monday.
"We really didn't want to vote for it. But we made a mistake, and now we're trying to do what's right and correct it."
But supporters, framing it as only a modest update on the state's existing religious freedom law, had pushed Ms Brewer to sign it in support of religious liberty.
The president of a conservative policy organisation that backed the bill said Ms Brewer's veto "marks a sad day for Arizonans who cherish and understand religious liberty".
"Opponents were desperate to distort this bill rather than debate the merits," Center for Arizona Policy president Cathi Herrod said in statement. "Essentially, they succeeded in getting a veto of a bill that does not even exist."
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