Wilson, who can also play in midfield, was injured in an FA Cup tie for Stoke City against Crystal Palace in January.
Manager Martin O'Neill said on Monday the 24-cap player had suffered a setback and would not make the squad.
Wilson's last Republic appearance was as a substitute in the 1-1 play-off draw in Bosnia-Herzegovina in November.
The 28-year-old made his debut in 2011 for the Republic, who play the Netherlands in Dublin on Friday night then Belarus on 31 May.
Their first match at the tournament is against Sweden in Paris on 13 June, with Belgium and Italy their other opponents in Group E.
Republic of Ireland defender Marc Wilson has been ruled out of Euro 2016 in France after failing to recover from a knee injury in time.