Vukić started out at his hometown club Proleter Zrenjanin, making his senior debut in the 1996–97 season, aged 17.

After spending almost two years with Atlético's B team, playing in the Segunda División, Vukić returned to his homeland and signed with Partizan in April 2000.

In January 2006, Vukić found himself back in familiar territory, having been loaned to his former club Partizan for the rest of the 2005–06 season.

Unfortunately, Vukić broke a foot in a friendly game against Ural Yekaterinburg,[8] managing to play just two competitive matches after a long pause.

[13] He helped Partizan win the double, scoring from the penalty spot in the Serbian Cup final against Vojvodina.

[22] He played three matches in the Super League Greece until the end of the 2012–13 regular season, scoring two goals in his first two appearances for the club against Panionios and Panathinaikos.

[23] On 26 April 2014, Vukić was the only scorer for his team in the Greek Cup final, converting a penalty in the 70th minute of their 4–1 loss to Panathinaikos.

[26] Vukić earned 26 caps for Serbia and Montenegro, making his full international debut in a 2–2 home draw with Azerbaijan on 12 February 2003.

[28] Vukić was a regular member of the team during the 2006 FIFA World Cup qualification, scoring four goals in the process.

He was included in the final 23-man squad for the 2006 FIFA World Cup, despite having been in the process of convalescence after a long break due to foot injury.