Gov. Jan Brewer has not indicated if she will sign the bill, saying she hasn't had a chance to review it, the Los Angeles Times reported Thursday.
The measure would allow a religious person to freely practice their religion.
Republican Rep. Steve Yarbrough, who introduced the bill, said the legislation maintained legal protections against discrimination
Opponents decried the bill as unconstitutional and divisive.
Shannon Minter, legal director of the National Center for Lesbian Rights, said the bill was "blatantly unconstitutional."
It passed the state House Thursday after being approved by the Senate on Wednesday.