The unnamed Irishman was one of four divers caught on the wreck as they attempted to remove memorabilia.
The 35-year-old is employed by the salvage group Titan and was arrested along with three colleagues, two South Africans and a Briton.
Their employer had won the contract to raise the Concordia from the seabed after it tragically went aground last year.
The Irish Sun reports that the men were reportedly spotted on CCTV cameras positioned around the vessel.
The Titan group has confirmed that it has dismissed all four employees.
The four men have been freed on bail by authorities in Grosseto until they appear before a court at a later date accused of theft and of breaching a sealed crime zone.
Italian police spokeswoman Elisabette Spoti said: “The men were spotted on CCTV and the security firm employed alerted us and Titan as to their unauthorized presence.
“The suspicion is they were trying to take items from the ship as souvenirs. They should not have been anywhere near the vessel as it is still a crime scene and as such is sealed off.
“The men had in their possession a rucksack with the Costa Concordia emblem on it. They had no permission to be on the ship.
“The incident was caught on camera at 1:30am when no salvage operation was ongoing. They were found on Deck 8, an area with several outside cabins as well as executive staterooms, all of which have safes inside.”
The luxury Costa Concordia liner was carrying more than 4,000 passengers and crew when it struck a reef off Giglio in January 2012 after captain Francesco Schettino changed course to carry out a sail by salute. Thirty-two people died in the disaster.