The lawsuit argues that Arizona's new measure requiring state and local police to question and possibly arrest illegal immigrants during the enforcement of other laws usurps federal authority.
Tuesday's action has been expected for weeks. President Barack Obama has called the state law misguided. Supporters say it is a reasonable reaction to federal inaction on immigration.
The government will likely seek an injunction to delay the July 29 implementation of the law until the case is resolved.
The government contends that the Arizona law violates the supremacy clause of the Constitution, a legal theory that says federal laws override state laws.
It is already illegal under federal law to be in the country illegally, but Arizona is the first state to make it a state crime and add its own punishment and enforcement tactics.
The /*L.A. County Board of Supervisors*/ voted 3 to 2 in favor of a boycott of Arizona in a meeting on June 1.
Reaction to the announcement of the lawsuit came swiftly and forcefully in Arizona.
"I am not going to be intimidated by the Department of Justice," said /*Maricopa County Sheriff Joe Arpaio*/.
Arpaio told the U.S. Attorney General to "bring on the lawyers." The state is ready to fight.
The Department of Justice suit seeks to block Arizona Senate Bill 1070. That is the law that allows Arizona peace officers to question anyone they detain about their immigration status.
The federal lawsuit tells Arizona leaders that to do so oversteps a constitutional line.
"Congress cannot delegate that authority to the states," said Hector Villagra, legal director of ACLU-Southern California. "And the states cannot take that authority unto themselves."
?*California Senator Barbara Boxer*/ (D) hammered the same message at an event in Sylmar.
"If every state decides to do its own laws on immigration, there's going to be chaos," said Boxer. "What we said was, that the unintended consequence of this law is going to be higher crime rates, that law enforcement is very upset about it. And what we said was, we need comprehensive immigration reform."
"The /*U.S. Conference of Mayors*/ unanimously passed my resolution calling for the repeal of the Arizona law, and calling for comprehensive immigration reform," said /*Los Angeles Mayor Antonio Villaraigosa*/.
Yet Arizona residents widely support the law, according to polls, as a means of controlling immigrant-related crime that they say is out of control. Existing federal laws, they say, leave them in a lurch.
"I invite the president to come to the border and he can see for himself the absolute necessity of getting our borders secure before more violence spills over onto our side of the border," said /*Ariz. Senator John McCain*/ (R).
/*President Barack Obama*/ responded last week, calling for comprehensive immigration reform. He lashed out at Arizona's bill, calling it "ill-conceived" and "divisive."
"Laws like Arizona's put huge pressures on local law enforcement to enforce rules that ultimately are unenforceable," said Obama.
The Arizona law will take effect on July 29 unless a federal judge grants an injunction to stop it.
A hearing is expected as early as next week.
Arizona State Sen. Russell Pearce, the principal sponsor of the bill co-sponsored by dozens of fellow Republican legislators, denounced the reported lawsuit as "absolute insult to the rule of law" as well as to Arizona and its residents.
Arizona State Rep. Kyrsten Sinema, a Phoenix Democrat who opposes the law, said the suit should help settle questions over what states can do when they don't think federal laws are being adequately enforced.
Prior to seeing the lawsuit or receiving any official notification, /*Ariz. Gov. Jan Brewer*/'s spokesman called the reported decision to sue "a terribly bad decision."
The Associated Press contributed to this report