Italy forward Zaniolo suffers second Euro injury curse
"Unfortunately I have to give up on my dream of representing my country in a major competition," Zaniolo wrote on Instagram.
Zaniolo also missed the last European championship with a serious knee injury.
He picked his latest injury in Monday night's rousing 3-3 Premier League thriller with Liverpool that eventually sealed Champions League qualification for Villa.
The 24-year-old has 19 caps for Italy, scoring twice, with Azzurri coach Luciano Spalletti picking him for six of Italy's eight matches since taking over from Roberto Mancini in August last year.
Spalletti will announce next week the squad with which European champions Italy will defend their title in Germany, where they will face Spain, Croatia and Albania in the group stage.