Born in Bačko Dobro Polje, a village near Titov Vrbas, Vuković started in Red Star Belgrade's youth academy but lack of first team opportunities prompted a move to Rad in 2006.
On 28 August 2009 it was announced that Vuković would be loaned to PSV Eindhoven, with the prospect of a permanent signing at the end of the season.
[1] Vuković made his official debut for PSV on 22 October 2009, in the UEFA Europa League match against Copenhagen, coming on as a substitute for Erik Pieters in the 86th minute of the game.
On 9 April 2010 Vuković, who was playing for PSV on loan from Rad, has signed a three-year deal with the Dutch club.
[2] On 31 August 2013, he made his return to Serbia and signed a two-year contract with Serbian SuperLiga side Vojvodina.