"By enforcing this statute, Arizona would impose a 'distinct, unusual and extraordinary' burden on legal resident aliens."
The decision was a ruling on a lawsuit filed earlier this month by the US justice department. Bolton has said that the law was "awkward" in its wording, and that she doubted it could be properly enforced.
Her ruling held that only the federal government, not state governments, can set US immigration policy.
Jan Brewer, the Arizona governor, said that this was "a temporary bump in the road" and an appeal against the judge's decision would be filed.
"It's a temporary bump in the road, we will move forward, and I'm sure that after consultation with our counsel we will appeal"
"The bottom line is that we've known all along that it is the responsibility of the feds, and they haven't done their job, so we were going to help them do that."
"We will take a close look at every single element Judge (Susan) Bolton removed from the law, and we will soon file an expedited appeal at the United States Court of Appeals for the 9th Circuit," Brewer said.
The Mexican government praised the judge's decision and said it would carefully follow the process to suspend the law.
"It's a first step in the right direction," Patricia Espinosa, Mexico's foreign minister said.
She said Mexico was still concerned about the rights of its citizens in Arizona and was stepping up consular protections in the border state.
Arizona is believed to be home to up to half a million illegal immigrants, many of whom are from Mexico.
The Obama administration has pushed the US congress to pursue an immigration reform bill, but that legislation has stalled, largely because of Republican opposition.
"We would love for the congressional delegation from Arizona, and the senators there, to support comprehensive immigration reform," Jennifer Kottler, a policy director at Sojourners, a Christian advocacy group, said.
"That would address so many of the issues there."
The law was passed in April by Arizona's Republican-controlled legislature, which called it a necessary step to stop illegal immigration.
Opinion polls have showed that nearly 60 per cent of the US population supports the law.
It has been criticised by human rights groups, the Catholic Church and the Mexican government, and by Barack Obama, the US president, who called it "misguided".
Thousands of activists have planned a demonstration against the law in Arizona on Thursday. That rally is still expected to take place, despite the court's verdict.
"Even if it issues a temporary injunction ... we're still going ahead with our protests, because 21 other states want to follow Arizona's footsteps with racist laws" of their own, Paulina Gonzalez, a spokeswoman for the group organising the protest, said.
One group, the National Day Laborer Organising Network, plans to fill nearly a dozen buses with activists in Los Angeles. The buses will drive from there to Phoenix, the capital of Arizona.
Organisers say none of the people on the buses will carry identification papers.
"Thursday will be our national civil disobedience day, when we'll stand up to a racist, discriminatory and hypocritical measure," Pablo Alvarado, the director of the network, said.
Another group plans to block access to federal government offices in Phoenix.
One-third of the roughly 6.6 million people living in Arizona are foreign-born, and more than five per cent of the population is estimated to be illegal immigrants.