Born in Zagreb, Medić started his career in local clubs Kustošija and HAŠK, before moving on to play in top-tier U17 and U19 Croatian competitions for Hrvatski Dragovoljac and NK Zagreb, before going on trial and signing for Istra 1961 during his last year of eligibility as a youth player. In the Pula-based club, Medić made his senior debut in the Prva HNL coming on for David Puclin in for David Puclin in the 58th minute of their 2–0 away loss to Slaven Belupo.[4] Medić was capped only once more for the team, before leaving the club in the summer of 2017.
Initially signing for Lučko in the Druga HNL and playing a single match for them, Medić moved on in August 2017 to the high-flying third-tier club NK Vinogradar. During the winter pause Medić went on a trial with Dinamo Minsk, which did not pan out, and the player missed the second half of the season.[5]
In the summer of 2018, however, Medić made a move abroad, signing for 1. FC Nürnberg,[5] playing for their fourth-tier reserves. In 2019, he moved on a two-year loan to the 2. Bundesliga team SV Wehen Wiesbaden.[6] Relegated with the team, Medić remained with Wehen Wiesbaden despite the club's relegation to 3. Liga, and, becoming a key player for the team, the club made his move permanent, signing him on a contract until 2024.[7]
On 6 August 2023, Medić signed for Dutch club Ajax on a five-year deal.[9] On 12 August 2023, he scored a goal on his debut against Heracles Almelo.[10]
On 20 August 2024, Medić returned to Germany and joined VfL Bochum on loan with an option to buy.[11]
