Born in Podgorica, Yugoslavia (nowadays in Montenegro) as Milutin Ostojić[1][2] (Serbian Cyrillic: Милутин Остојић), Vujičić spent his childhood in Foča, Bosnia and Herzegovina.
[4] In February 2021, head coach Dejan Radonjić added Vujičić to the Crvena zvezda mts roster for the 2021 Radivoj Korać Cup tournament in Novi Sad.
[5][6] On 11 February, he made his debut for Crvena zvezda in a 108–47 win over Radnički Kragujevac, making 3 points, 3 assists and a rebound in 11 minutes of playing time.
[9][10] On 19 February, Vujičić was a member of the Zvezda roster for a EuroLeague game with Zenit Saint Petersburg without any played time.
[13] In January 2018, he was added to a 22-man preliminary roster of the Bosnia and Herzegovina national under-16 team for an international youth tournament in Sakarya, Turkey.