Vuković began his professional career at Montenegrin side FK Zeta signing for the club in 2003.

[1] Due to his fine long term form, Croatian giants HNK Hajduk Split signed him from the club in the summer of 2011 for a reported fee of €425,000.

He scored deciding goal against Neftchi which took Mladost to the second qualifying round of UEFA League Europa 2015.

In 2015–16 UEFA Europa League qualifiers, he scored decisive goal against Neftchi Baku which advanced Mladost to next round.

His senior debut for Montenegro came on November 18, 2009 when he came in as a substitute for Milorad Peković in a friendly match against Belarus.