The case involves Lavoni Kidd, who converted to Islam and changed his name to Abdullah al-Kidd.
Kidd, a former football star at the University of Idaho, was arrested and shackled at a Washington airport in 2003 and held as a "material witness," the Los Angeles Times said.
Kidd cooperated with the FBI after the Sept. 11, 2001, terror attacks, answering questions about another Muslim man in Idaho, the Times said.
He was arrested when he bought a round-trip ticket to Saudi Arabia, where he had a scholarship to study.
Kidd's complaint says he was shackled for two weeks, strip-searched repeatedly and the lights in his cell were kept on, the Times reported. He was eventually released but his U.S. passport was taken.
Kidd sue Ashcroft and other officials in 2005 and the lower federal courts refused to dismiss the suit.
SCOTUSBLOG.com said the Supreme Court agreed to review the case but limited the review to two issues: Whether Ashcroft was entitled to absolute immunity in a case involving detention under the federal material witness law, and whether he had immunity as attorney general to a Fourth Amendment claim.
The Fourth Amendment bans unreasonable search and seizures.
The justices agreed to hear the case next term. New Justice Elena Kagan did not participate in the consideration, presumably because she had some contact with the case as U.S. solicitor general.