Opponents of Arizona's proposed law asked Bolton to block the "papers please" requirement, claiming systematic racial profiling would result.
A U.S. Supreme Court ruling in June upheld the police requirement.
In her ruling, Bolton said the court will not ignore the clear direction from the Supreme Court that the provision "cannot be challenged further on its face before the law takes effect." She reiterated the high court's interpretation that the law might be able to be challenged as unconstitutional on other grounds.
Among the opponents of the law was the Obama administration, which challenged the law based on the argument that federal immigration law trumped Arizona law. The challenge didn't confront racial profiling. The administration failed to persuade the nation's highest court to strike down the questioning requirement.
To the supporters of Arizona's law, the questioning requirement was the most important part of the statute, whose stated purpose was to reduce the problems associated with illegal immigration through enforcement the state's policy.
Shortly before the law was to take effect in July 2010, Bolton prevented police from enforcing the questioning requirement and other parts of the statute, ruling the Obama administration would likely succeed in showing federal law trumps the state law.
Brewer, who signed the measure into law, appealed the ruling, lost at the 9th Circuit Court of Appeals and took her case to the Supreme Court.
Less controversial sections of the law have been in effect since late July 2010, but have rarely been used.
Arizona's law was passed amid voter frustration with the state's role as the busiest illegal entry point into the country. Five states - Alabama, Georgia, Indiana, South Carolina and Utah - have adopted variations on Arizona's law.
Brewer's office said the law is expected to go into effect shortly.
The Associated Press contributed to this report.
