The 20-year-old has not played this season and after Arsenal lost 2-1 at home to Wigan Athletic in the Premier League Gunners boss Arsene Wenger said he had no chance of being fit for the tournament in Poland and Ukraine starting in June.
"Jack Wilshere will not play again this season, and will not play at the Euros. He is making slow progress. He will not be ready. The FA know about Jack's injury," Wenger told the club website. "He is devastated."
Wilshere has made five England appearances since making his debut in 2010.