Simpson's body was found Sept. 17 near Edwards, Miss. She died of blunt force trauma.
James Cobb Hutto III, 39, of Jasper, was arrested in Alabama, allegedly while driving her car.
Hutto's attorney, Todd Crutchfield, did not return calls or e-mails seeking comment.
Hutto is wanted in two Alabama on charges of murder, attempted murder and armed robbery.
In Mississippi, Hinds County District Attorney Robert Shuler Smith said he will seek the death penalty. But the Mississippi attorney general's office told The Clarion-Ledger newspaper Hutto may go to Alabama to face charges first.