However, Brewer denied the accusations saying that she would "not tolerate racial discrimination or racial profiling in Arizona".
Earlier in the day, Obama said that the law would undermine American values.
"Our failure to act responsibly at the federal level will only open the door to irresponsibility by others," he said.
Al Jazeera's Monica Villamizar reports on Arizona's controversial new immigration law
"The recent efforts in Arizona threatened to undermine basic notions of fairness that we cherish as Americans."
Obama was addressing a ceremony at the White House in which 24 members of the US military, originally from China, Mexico, Ethiopia and other countries became American citizens.
"Today we celebrate the very essence of the country that we all love - an America where so many of our forebearers came from someplace else," Obama, whose father was Kenyan, said
He warned that the Arizona bill could harm trust between police officers and their communities and said his administration would take a close look at it.
"Obama is saying that in the interest of the country and the workforce, we need to fix our immigration system," Ali Noorani, executive director of the National Immigration Forum in Washington, told Al Jazeera.
"This is a dagger in the heart of Arizona's economy and does nothing to keep Arizona safer."
Obama warned that without federal immigration reform the door would be open to "misguided efforts" such as the recent measure in Arizona that has raised questions of civil rights.
"This is a dagger in the heart of Arizona's economy"
Ali Noorani, director of the National Immigration Forum
"The majority of America wants comprehensive immigration reform and Obama is beginning to lead the way. I don't think that there is any support for this type of law in the rest of the country," Noorani said.
The bill is one of the toughest laws in the country designed to curtail illegal immigration.
Critics say it carries the potential to turn neighbours against neighbours by allowing citizens to compel police to comply with the law, preventing them from avoiding the issue in order to retain the trust of immigrants.
Given the long border between Arizona and Mexico, the state has a history of tough laws that have been unsuccessful in deterring undocumented immigrants from making the short, but often perilous, journey across the desert border region.
Obama has promised advocates who want a path to legal status for 11 million illegal migrants that he will take up the issue, but only if he wins Republican support.
But in an election year and with 9.7 per cent unemployment many observers doubt whether the political momentum can be found for action on such a controversial issue.