The 20-year-old, who last week was said to be making slow progress in his bid to overcome an ankle injury, will also miss the rest of the Gunners' season.
Speaking after his side lost 2-1 at home to Wigan Athletic, Wenger explained: "Jack Wilshere will not play again this season and will not go to the Euros, that is for sure.
"He is not ready to practise 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."
Wilshere has not featured at all this season.