Ognjen grew up with Crvena zvezda youth teams and signed his first professional contract in December 2012.

[1] Dobrić signed a four-year deal with KK Crvena zvezda on 21 September 2016,[2] after previously playing on loan for FMP for three seasons.

[10] During the 2022–2023 campaign, in 31 EuroLeague games (19 starts), he averaged 9.9 points, 2.5 rebounds and 1.6 assists, playing around 24 minutes per contest.

In July 2023, Dobrić signed a two-year deal with Virtus Bologna, of the Italian Lega Basket Serie A (LBA) and the EuroLeague.

On 24 September 2023, after having ousted Olimpia Milano in the semifinals, Virtus won its fourth Supercup, and the third in a row, defeating 97–60 Germani Brescia.