He was part of the Swiss squad for the 2010 FIFA World Cup, playing the last 13 minutes of the group match against Chile after coming on for Gelson Fernandes. Bunjaku played in Kosovo's first FIFA-approved match, against Haiti in a 0–0 home friendly on 5 March 2014. Bunjaku played for Kosovo against Turkey on 21 May 2014 and scored its first international goal.