She played for in the 2010 Olympics. It was the first time that Slovakia competed in women's ice hockey outside of Europe. Of note, she was the captain of the Slovak national team at the 2010 Vancouver Winter Games. Her first Olympic women's ice hockey game came on February 13, 2010 against . Slovakia lost the game by an 18-0 mark. Her first Olympic points came on February 20, 2010. Veličková assisted on both goals in a 4-2 loss to . She would finish with three assists in the Olympic tournament as Slovakia finished in eighth place.