The 5.8 magnitude quake is the second in the space of a week in the northern region of Emilia Romagna.
It has led to the warm-up game between Italy and Luxembourg, scheduled to be played on Tuesday night at the Stadio Tardini in Parma, being called off.
"In our region, millions of people have been affected - in view of the victims and of the continuous tremors, it does not seem appropriate to proceed with the game," the region's president, Vincenzo Bernazzoli, said.
It comes as Giovanni Trapattoni named his final squad for the tournament - with Paul McShane being drafted in, in place of injured Kevin Foley.
Keeper Shay Given and defender John O'Shea have made the cut, despite also nursing injuries.
"With the injuries that we experienced in the squad over the past week, I have had to make a tough decision when it comes to naming the 23 players that must be submitted to UEFA for the championship," Trap said.
"Kevin Foley, John O'Shea, Paul McShane, Darren O'Dea, Shay Given had all been carrying knocks and we have been monitoring them closely in their recovery."
Ironically, Foley trained with the team on Monday night, while McShane didn't after suffering a bruised heel during Saturday's 1-0 friendly victory over Bosnia-Herzegovina in Dublin.
With regards to Foley, who had been hoping to recover in time, the manager added: "I have spoken to him and understand how difficult it is, saying that he can remain with the squad if he wishes."
The Republic are due to first play in the finals against Croatia on 10 June.
Italy have also named their final Euro 2012 squad - including Juventus defender Leonardo Bonucci, despite his expected questioning over the latest match-fixing scandal to hit Italian football.
He's not under formal investigation at this stage and has denied any wrongdoing, but it's thought he'll face questions over his time as a Bari player during the 2009-10 season.
Zenit St Petersburg defender Domenico Criscito was left out of the Italian squad, after he was questioned by police as part of the same probe.
The Euro 2012 tournament is being co-hosted by Poland and neighbouring Ukraine, where security is being stepped up amid fears over violence.
Polish police have already arrested 42 gang members, some of whom will be questioned over suspected involvement in disorder between fans of local league football clubs.
Republic of Ireland squad
1. Shay Given (Aston Villa), 2. Sean St Ledger (Leicester), 3. Stephen Ward (Wolves), 4. John O'Shea (Sunderland), 5. Richard Dunne (Aston Villa), 6. Glenn Whelan (Stoke), 7. Aiden McGeady (Spartal Moscow), 8. Keith Andrews (West Brom), 9. Kevin Doyle (Wolves), 10. Robbie Keane (LA Galaxy), 11. Damien Duff (Fulham), 12. Stephen Kelly (Fulham), 13. Paul McShane (Hull), 14. Jonathan Walters (Stoke), 15. Darron Gibson (Everton), 16. Keiren Westwood (Sunderland), 17. Stephen Hunt (Wolves), 18. Darren O'Dea (Celtic), 19. Shane Long (West Brom), 20. Simon Cox (West Brom), 21. Paul Green (Derby), 22. James McClean (Sunderland), 23. David Forde (Millwall).