Junuzović moved with his parents to Austria when he was five years old. Before his 12th birthday, they went on to Graz, where he soon played for the youth teams of GAK. Junuzović became an Austrian citizen as youth.
Being 17 years old, he played first time for GAK in the Bundesliga in spring 2005. In 2006 he was called to play for the ÖFB-Team and he had been a regular starter for GAK. In summer 2007 he moved to SK Austria Kärnten. In summer 2009, Junuzović moved to Austrian giants FK Austria Wien.
In 2010, Junuzović was awarded two awards for his performances with Austria Wien and the national team: the managers of the Austrian Bundesliga voted him the 'Austrian Player of the Year' and the country's supporters voted him 'Player of the Year' in the annual award awarded by the Kronen Zeitung.