A right-footed midfielder, Kurtić joined the 1. SNL club Gorica in August 2010 from the 2. SNL club Bela Krajina. His stint at Gorica lasted only six months, as he was noted by scouts of Serie A club Palermo; on 18 December 2010 it was announced Kurtić had agreed a four-and-a-half year contract with the Sicilians, effective from January 2011, thus making him the fourth Slovenian to join the rosanero during the 2010–11 season. On 12 January 2011, Kurtić made his debut in a Palermo jersey, playing 63 minutes in the Coppa ItaliaRound of 16 game against Chievo; the match ended in a 1–0 win for the Sicilians. On 13 February 2011, Kurtić made his debut in Serie A, playing the whole 90 minutes against Fiorentina; the match ended in a 2–4 win for the Tuscans. On 10 April 2011, Kurtić scored his first goal in Serie A for Palermo against Cesena. On 1 August 2011, he moved on loan to Varese in Serie B, with an option for his new club to acquire 50% of his transfer rights by the end of the season. He debuted for the team in Serie B on 27 August against Bari. For the 2012–13 season he returned to Palermo.
On 1 July 2013, Kurtić moved to Sassuolo in co-ownership for €2.5 million. He made his Sassuolo debut in the third round of Coppa Italia away to Novara on 17 August 2013, as a starter. On 30 January 2014, he moved to Torino on loan, also at the decision of Palermo, who owned half of his player rights. He scored his first goal for Torino on 18 April 2014 in the 34th round away to Lazio. During the season, he collected 16 appearances and scored two goals in the league. On 20 June 2014, his co-ownership agreement between Palermo and Sassuolo was resolved in favour of Sassuolo for an additional €1.4 million. On 1 September 2014, he moved on loan to Fiorentina. He made his debut on 18 September in the UEFA Europa League match against Guingamp, and scored his first goal on 21 September against Atalanta.
On 10 January 2020, he joined Parma on loan until the end of the 2019–20 season, at the end of which Parma is obligated to buy his rights. He signed a contract with the club until 30 June 2023.
International career
Kurtić was a member of the Slovenia U21 team, appearing in two friendlies in 2009. He made his senior debut against Greece on 26 May 2012, scoring a goal from a free kick.
