West Ham defender Angelo Ogbonna, Manchester United full-back Matteo Darmian and Southampton striker Graziano Pelle are all included.
Veteran midfielder Andrea Pirlo and AC Milan striker Mario Balotelli had already been left out by Antonio Conte.
New York City's Pirlo, 37, has not been picked by the Azzurri since September's qualifying win over Bulgaria.
Balotelli, 25, scored one league goal in a season-long loan from Liverpool.
Italy coach Conte, who will become Chelsea boss after the tournament, was strongly tipped to include Napoli's Jorginho after Juventus midfielder Claudio Marchisio and Paris St-Germain's Marco Verratti were ruled out.
AC Milan's Montolivo has been struggling with a calf problem.
The Euro 2012 runners-up have been drawn alongside Belgium, Sweden, and the Republic of Ireland in Group E.
Euro 2016, which is being hosted by France, starts on 10 June and runs until 10 July.
Goalkeepers: Gianluigi Buffon (Juventus), Federico Marchetti (Lazio), Salvatore Sirigu (Paris St-Germain)
Defenders: Andrea Barzagli (Juventus), Leonardo Bonucci (Juventus), Giorgio Chiellini (Juventus), Angelo Ogbonna (West Ham)
Wingers: Federico Bernardeschi (Fiorentina), Antonio Candreva (Lazio), Matteo Darmian (Manchester United), Mattia de Sciglio (Milan), Stephan El Shaarawy (Roma)
Midfielders: Daniele de Rossi (Roma), Alessandro Florenzi (Roma), Emanuele Giaccherini (Bologna), Thiago Motta (Paris St-Germain), Marco Parolo (Lazio), Stefano Sturaro (Juventus)
Forwards: Eder (Inter), Ciro Immobile (Torino), Lorenzo Insigne (Napoli), Graziano Pelle (Southampton), Simone Zaza (Juventus)
Italy have left midfielders Jorginho and Riccardo Montolivo out of their 23-man squad for Euro 2016.