Born in Hrvatska Dubica, Braun began playing as a youngster for the local club NK Una.
After impressing Dinamo's manager Márton Bukovi he signed for the Blues and quickly went on to establish himself as a regular member of the team's defensive line in the 1961–62 season.
Led by the prolific goalscorer Slaven Zambata the team also finished runners up in the 1962–63 Yugoslav First League.
at Maksimir Stadium – although Celtic progressed through due to the Scots' earlier 3–0 win in Glasgow.
Although Braun's club teammate Zambata scored to put Yugoslavia 1–0 up in the opening minutes, the game eventually ended in a 3–2 defeat.