Milinković came through the youth system of Partizan, before starting his senior career at lower league club Mladost Petrinja.
Milinković also played for Mogren, Borac Banja Luka, Radnički Niš, Kispest-Honvéd, Tosu Futures, Waregem, Nice, Hansa Rostock, Anorthosis Famagusta and Doxa Katokopia.
He began the 2015–16 season in a win over Dila Gori in the second qualifying round for the UEFA Champions League on 14 July 2015.
In the Serbian SuperLiga he also had a great start, defeating Metalac Gornji Milanovac 4–0, while in the second round Partizan won against Jagodina 6–0.
On 26 August 2015, Milinković's Partizan was defeated by BATE Borisov and as a result entered the group stage of the UEFA Europa League.