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.

On 8 July 2015, Babić signed a four-year contract with Spanish side Real Sociedad, being assigned to the reserves in Segunda División B.

[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.

[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.