Zabavník played for MFK Košice and MŠK Žilina in his native country's Corgoň Liga, winning the championship twice with MŠK Žilina. Between 2004 and late 2005, Zabavník played in Bulgaria for PFC CSKA Sofia. In the end of 2005, he was sold to Sparta Prague. In February 2008, Sparta Prague sold Zabavník to Terek Grozny. In December 2009, he was released and signed for 1. FSV Mainz 05 on 1 February 2010. The signing proved to be astute business by Mainz 05 as Zabavník went on to make a string of impressive performances for them cementing his place in the starting eleven.