During his playing career in the 1950s, Konjović was on Belgrade-based teams Crvena zvezda and Partizan of the Yugoslav Federal League and two of the biggest and most popular clubs in Serbia.
[1] Konjović won three Yugoslav Championships with the Zvezda team coached by Nebojša Popović.
During this stint he played with Milan Bjegojević, Đorđe Andrijašević, Ladislav Demšar, Srđan Kalember, and Borislav Ćurčić.
[2][3] Konjović was a member of the Yugoslavia national team that participated at the 1954 FIBA World Championship.
[5] Konjović was the first player taller than 2 m (6 ft 7 in) who played for Yugoslavia.