Babić started out at his hometown club Borac Banja Luka, before joining the youth system of Vojvodina in August 2011. He made his first team debut under manager Branko Babić on 1 March 2014, playing the full 90 minutes in a 2–0 home win over Voždovac.[3] Despite making only eight league appearances in the 2013–14 season, Babić was named in the competition's best eleven. He also helped his team win the Serbian Cup, scoring a goal in a 2–0 victory over Jagodina in the final.[4] In the 2014–15 season, Babić was a regular choice at centre-back, making 27 appearances in all competitions.
On 31 August 2016, Babić was loaned to Segunda División club Reus Deportiu, on a season-long loan.[6] A backup option to Pichu Atienza and Jesús Olmo, he featured in eleven matches, and also scored his first professional goal while at the club, netting his team's only in a 1–2 home loss against Córdoba on 4 December.
Red Star Belgrade
On 7 July 2017, Babić made a one-year loan deal with Serbian SuperLiga club Red Star Belgrade.[7] In the mid-season of the 2017–18 campaign, Red Star purchased his contract and Babić signed with the club permanently for a fee of €800,000.[8] On 9 February 2018, Babić signed a new four-year contract with Red Star Belgrade.[9] Babić scored his first goal for Red Star in 5–2 away victory over Mladost Lučani on 1 April 2018, on Slavoljub Srnić's assist from corner kick.[10] On 12 August 2018, Babić scored in 3–0 home win against Spartak Subotica.[11]
Almería
On 30 August 2021, Babić returned to Spain after agreeing to a one-year loan deal with UD Almería in the second division.[12] The following 5 June, after contributing with the club's promotion to La Liga as champions, he signed a permanent contract until 2026.[13]
^Babić spent the first half-season as a loaned player making 14 league, 1 cup and 3 continental appearances,[7] after which he joined the club permanently[8]