The motion for a preliminary injunction follows its class action lawsuit filed earlier this month. Judges have already blocked key parts of other immigration laws passed in Georgia, Arizona, Utah and Indiana.
Critics say the Alabama law, due to take effect on September 1, is unconstitutional on multiple grounds.
"It will criminalize Alabamians for everyday interactions with people who are here without documents, such as driving someone to the grocery store or to church," said Olivia Turner, executive director of the American Civil Liberties Union of Alabama.
"Law enforcement officers will be required to violate the constitutional rights of citizens and non-citizens alike," she added.
Under the Alabama law, police must detain someone they suspect of being in the country illegally if the person cannot produce proper documentation when stopped for any reason.
The law would also make it a crime to knowingly transport or harbor someone who was in the country illegally.
Alabama's law is unique in requiring public schools to determine, by review of birth certificates or sworn affidavits, the legal residency status of students upon enrollment.
The civil rights groups' lawsuit says that provision will deter children in immigrant families from enrolling in public schools.
The sponsors of the Alabama law said they were confident it would withstand the legal challenge. Alabama House Majority Leader Micky Hammon said the state would continue its fight against illegal immigration, even if an injunction is granted.
"These far-left, liberal groups have filed (for) an injunction because those who live here illegally and break our laws with their simple presence are packing up and leaving Alabama," said Hammon, a Republican and principle sponsor of the law.
"That was the intent of the bill in the first place, to protect our borders and our jobs."