Hodžić started playing football at his hometown club Željezničar, before joining the youth academy of English team Liverpool in May 2011.
[6] In May 2014, Hodžić signed a five-year deal with Croatian side Dinamo Zagreb.
[7] He made his official debut for the team in a Croatian Cup game against Istra 1961 on 12 February 2015.
[16] In August, Hodžić was transferred to Hungarian outfit Fehérvár for an undisclosed fee.
[17] He made his competitive debut for the side in a UEFA Europa League tie against Bate Borisov on 20 September.
[28] In September 2015, he received his first senior call-up, for UEFA Euro 2016 qualifiers against Wales and Cyprus,[29] but had to wait until 29 May 2016 to make his debut in a friendly game against Spain.
[30] On 12 October 2019, in a UEFA Euro 2020 qualifier against Finland, Hodžić scored his first senior international goal.
[31] Hodžić is a practising Muslim; together with international teammates Ibrahim Šehić, Muhamed Bešić, Izet Hajrović, Sead Kolašinac, Edin Višća and Ervin Zukanović he visited a mosque in Zenica during the national team's concentration.