Wolverhampton Wanderers defender Foley was named in the original party for the trip to Poland and the Ukraine earlier this month but only trained with the squad for the first time on Sunday after suffering from a hamstring injury.
"Although Kevin has been recovering well, I have made the difficult decision to leave him out of the 23-player list after completing fitness tests on John O'Shea and Paul McShane this morning," Trapattoni said in a statement.
"I have spoken to him and understand how difficult it is, saying that he can remain with the squad if he wishes."
The only other change from the original squad saw Derby County midfielder Paul Green replace Keith Fahey on Saturday after the Birmingham City utility midfielder was ruled out with a groin injury.
Ireland begin their campaign, their first appearance at a major championship for ten years, on June 10 against Croatia before facing Spain and Italy in a tough Group C.
Squad:
Goalkeepers: Shay Given (Aston Villa), Keiren Westwood (Sunderland), David Forde (Millwall).
Defenders: John O'Shea (Sunderland), Richard Dunne (Aston Villa), Sean St Ledger (Leicester City), Stephen Ward (Wolverhampton Wanderers), Paul McShane (Hull City), Stephen Kelly (Fulham), Darren O'Dea (Celtic).
Midfielders: Keith Andrews (West Bromwich Albion), Glenn Whelan (Stoke City), Darron Gibson (Everton), Damien Duff (Fulham), Aiden McGeady (Spartak Moscow), Stephen Hunt (Wolverhampton Wanderers), Paul Green (Derby County) James McClean (Sunderland).
Forwards: Robbie Keane (LA Galaxy), Kevin Doyle (Wolverhampton Wanderers), Simon Cox (West Bromwich Albion), Jonathan Walters (Stoke City), Shane Long (West Bromwich Albion).
