The diver, identified as Israel Franco Moreno, 40, of Spain, apparently was cut on his leg by sheet metal while working to install flotation devices that will be used to right the capsized vessel, the Italian news agency ANSA reported.
He is the first person to die during a work-related accident during the salvage operation, ANSA said.
The Costa Concordia ran into rocks off Giglio Island on Jan. 13, 2012, killing 30 people and leaving two others missing and presumed dead. The ship's captain, Francesco Schettino, is on trial, charged with multiple counts of manslaughter and dereliction of duty.
Plans are for the ship to be removed from the rocks this coming summer.