Born in Kraljevo, Dudić started out at local club Magnohrom before briefly joining the youth system of Red Star Belgrade.

He spent four and a half years with the club, winning two championships and three national cups.

In 2006, Dudić moved abroad and signed with Austrian club Red Bull Salzburg.

In 2011, Dudić switched to fellow Bundesliga side Sturm Graz.

At international level, Dudić was capped 13 times for Serbia and Montenegro, making his debut in 2001.