As the son of former Washington Diplomats midfielder Aleksandar "Alex" Mihailović,[4] Djordje was introduced to soccer at an early age.

[9] During the Knockout Round clash with the New York Red Bulls, Mihailovic was diagnosed with a ruptured ACL after a tackle that left him in serious pain.

[12] On August 24, 2022, Montreal announced a transfer had been agreed with Eredivisie side AZ for Mihailovic, effective January 1, 2023.

[14] On January 8, 2024, Mihailovic returned to the United States, joining Colorado Rapids for a reported transfer fee of around $3 million.

Mihailovic was included on the 23 man roster for the 2019 CONCACAF Gold Cup where he made two appearances during the group stage.