Kubiak was first selected to represent the Polish national team by coach Andrea Anastasi in 2011. With the Polish team, he won three medals in 2011 - silver at the World Cup and two bronzes at the World League and the European Championship. He was a gold medalist at the World League 2012 in Sofia, Bulgary. On 16 August 2014 he was selected to the Polish squad at the World Championship held in Poland. On 21 September 2014 Poland won the title of World Champion 2014. On 27 October 2014 he received a state award granted by the Polish President Bronisław Komorowski, the Gold Cross of Merit "for outstanding sports achievements and promoting Poland in the world".