Vittek, 33, who is Slovakia's all-time top scorer with 23 goals, is injured.
Liverpool's Martin Skrtel is included in the squad after his injury-hit campaign in the Premier League.
Slovakia face Wales, Russia and England in Group B at the finals in France, with their first game against Chris Coleman's side on 11 June.
"The players' names for the nomination were clear so I had no reason to speculate," Kozak said.
Goalkeepers: Matus Kozacik, Jan Mucha, Jan Novota
Defenders: Peter Pekarik, Milan Skriniar, Martin Skrtel, Norbert Gyoember, Jan Durica, Kornel Salata, Tomas Hubocan, Dusan Svento, Lukas Tesak
Midfielders: Viktor Pecovsky, Matus Bero, Robert Mak, Erik Sabo, Juraj Kucka, Patrik Hrosovsky, Jan Gregus, Stanislav Sestak, Marek Hamsik, Ondrej Duda, Miroslav Stoch, Vladimir Weiss
Forwards: Michal Duris, Adam Nemec, Adam Zrelak
Striker Robert Vittek is the headline absentee from the provisional 27-man squad Slovakia coach Jan Kozak has named for Euro 2016.