A stress fracture to his right ankle has prevented Wilshere from playing this season.
Speaking after Arsenal's surprise 2-1 loss at home to Wigan in the Barclays Premier League on Monday night, Wenger said: "Jack Wilshere will not play again this season and will not go to the Euros, that is for sure.
"He is not ready to practice today or next week. He makes progress, but slow progress.
"What is for sure is he will not be ready for the end of the season and not for the Euros.
"He is devastated, and you can understand that."