 On 10 December 2006, Kozáčik made his debut for Slovakia when he played in the first half of a friendly against the United Arab Emirates.However, his next game for the national team came almost seven years later when he started in a 2014 World Cup qualifier against Latvia.Kozáčik had been Slovakia's number one goalkeeper in the successful qualification campaign for UEFA Euro 2016 qualifying and was the first choice of coach Ján Kozák.