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.[3] He scored his ABA League high score of 17 points against KK Olimpija Ljubljana,[4] and his Euroleague high of 17 points in loss to Baskonia Vitoria Gasteiz.[5] On 6 July 2019, Dobrić signed a two-year contract extension for the Zvezda.[6] He averaged 5.1 points per game. On 8 September 2020, Dobrić signed a two-year contract extension with the Zvezda.[7][8] On 12 December 2020, Dobrić recorded his 250 apperiences for the Zvezda.[9] He re-signed with the team on 6 July 2021.[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.