Kozák has also won eighteen medals at the ICF Canoe Sprint World Championships with fourteen golds (K-1 500 m: 2013, 2014, 2018; K-2 200 m: 2011; K-2 500 m: 2009, 2010, 2015, 2018; K-4 500 m: 2009, 2011, 2013, 2014, 2018 and K-1 200 m relay: 2013), two silvers (K-1 500 m: 2011 and K-4 500 m: 2015) and two bronzes (K-1 500 m: 2019, K-2 1000 m: 2007).