In upholding the police checks, Kennedy said their mandatory nature did not interfere with the federal immigration scheme, and found unpersuasive the Obama administration argument that federal law preempted this part of the law at this stage.
He said it was improper to block that provision before state courts had an opportunity to review it, and without some showing that its enforcement conflicted with federal immigration law.
Kennedy also left open the possibility for constitutional or other challenges to the law once it goes into effect.
Opponents of the Arizona law also have sued on other grounds that it was unconstitutional and could lead to ethnic and racial profiling of the fast-growing Hispanic population, which represents 16 percent of all Americans.
The ruling went to the heart of a fierce national debate between Democrats and Republicans over the 11.5 million illegal immigrants the U.S. government estimates to be in the country.
The ruling upholding the police checks was a win for Arizona Republican Governor Jan Brewer, who championed the measure and called the decision a "victory for the rule of law."
Republican presidential candidate Mitt Romney, who challenges Obama in the November 6 U.S. election, had opposed the federal government's challenge to the law.
"Today's decision underscores the need for a president who will lead on this critical issue and work in a bipartisan fashion to pursue a national immigration strategy," Romney said in a statement.
SCALIA ANGRILY DISSENTS
Justice Antonin Scalia read an angry dissent from the bench, saying he would have upheld the entire Arizona law. It "boggles the mind" that the president might decline to enforce federal immigration law, Scalia said in apparent reference to Obama's June 15 executive order stopping deportation for certain young people in the United States illegally.
Obama has vowed to push for comprehensive immigration legislation if re-elected on November 6. Opinion polls show Hispanics, now equal to 16 percent of all Americans, overwhelmingly support Obama. Most illegal immigrants are Hispanics.
Arizona, on the southwest border with Mexico, two years ago became the first of half a dozen U.S. states to adopt laws to drive illegal immigrants out. About 360,000 of the country's illegal immigrants, or 3 percent, reside in Arizona. Most of the state's nearly 2 million Hispanics are in the country legally.
The immigration dispute was widely viewed as the second most important case in the Supreme Court's 2011-12 term, behind only the historic legal battle over Obama's healthcare overhaul law. A ruling in that case is expected on Thursday.