Subotić was born in Zagreb, SR Croatia, but his family originated from Doboj, Bosnia and Herzegovina, all back then part of Yugoslavia.

[2] His younger brother Dejan (born in 1996) is also footballer, having signed his first professional contract in 2018 with Serbian club FK Rad.

[4] The following season he advanced to their U-21 team, who played in the third tier, and they won their division (group B) and became Swiss champions at U-21 level.

[11] In February 2011, Danijel Subotić signed a contract with the Romanian club FC Universitatea Craiova of Liga 1.

In July 2011, Subotić went on trial with Scottish Premier League side St Johnstone, where he played in one friendly match in an attempt to win a contract.

On 23 July 2015, Subotić signed for Moldovan side Sheriff Tiraspol,[18] leaving the club by mutual consent on 28 January 2017.

Together with his Basel team-mates Oliver Klaus, Fabian Frei, Valentin Stocker, Dominik Ritter, Michel Morganella and Pascal Schürpf, Subotić played in the Switzerland U-19 team during the 2008 UEFA European Under-19 Football Championship qualification.