Career
Barbarić came through youth ranks of, joining the senior squad during the Prva HNL winter break in 2008. He made 5 appearances, of which on three occasions he started in the first-eleven. During the summer transfer window he agreed to join Dinamo"s affiliate Lokomotiva on a six–months loan.
He featured in 13 out of 15 league matches and scored 1 goal before he returned to Dinamo in January 2009.
By the end of the season he appeared 6 times in the league and 2 times in Croatian Cup. Barbarić established himself as a first–team regular at the start of the 2009-2010 season, as the centre–back Robert Kovač missed all of the early season matches due to an injury.
On June 27, 2015, Barbarić signed a two-year contract with FK Sarajevo. Barbarić is a part of Croatia under–21 national team
His first cap at the under–21 level came on 1 October 2008 in a match against Slovenia.
He was also capped at under–17 and under–19 levels.