The ruling means local law enforcement officers can now check the immigration status of people stopped during an investigation of possible crimes, The Arizona Republic reported.
In her ruling denying the injunction, U.S. District Judge Susan Bolton said Wednesday she would not "ignore the clear direction" of a June 28 ruling by the Supreme Court that the law would have to go into effect to determine if it infringed on people's civil liberties.
Bolton temporarily stopped enforcement of another provision that made it illegal to transport or harbor anyone suspected of being in the country illegally. She ruled that provision was pre-empted by federal law.
A coalition of civil rights groups had requested both injunctions.
Gov. Jan Brewer, who signed the bill in 2010, praised the court's decision.
At a news conference, she said the law "must be enforced fairly, effectively and without compromising civil rights or the Constitution."
She added: "I know the world is watching. But I know that our state and local officers are up to the task."
Civil rights cautioned they would be watching how the law was enforced.
"If we find that the law as implemented violates the Constitution in any fashion, we'll certainly be back in court," said Karen Tumlin of the National Immigration Center, one of the groups that requested the injunction.