Milunović made his professional debut with hometown club Borac Čačak, but saw little playing time.

On 16 September 2015, he scored BATE's only goal in their first Champions League match that season, a 4–1 loss against Bayer Leverkusen.

[3] Although BATE was last in their group by the end of the 2015 UEFA Champions League group stage, BATE's general secretary Andrei Vashkevich stated that Milunović was one of the team's most consistent players, even suggesting that he had a chance to be named the Vysheyshaya Liga's Player of the Year.

[4] Milunović was subsequently named in the ideal team of the Belarus's Vysheyshaya Liga for two consecutive seasons.

[6] Milunović made his first appearance for the Serbia national football team under coach Slavoljub Muslin in a 2-1 friendly win over Cyprus in November 2016.