Senior career
In August 2012, Kovačić received his first competitive call-up for the Croatian senior team match against Switzerland, but did not play because of injury. Subsequently, he received a call up for 2014 FIFA World Cup qualification matches in March 2013. He made his senior debut in a qualification match against Serbia on 22 March, playing as a central midfielder alongside Luka Modrić, instead of a regular team starter, Ognjen Vukojević. Four days later, he played against Wales at the Liberty Stadium, coming on as a second-half substitute in a 1–2 win. His third match of the campaign came in June, when Croatia faced Scotland in Zagreb and suffered a frustrating defeat as they were unable to score despite a string of good chances. By the end of the qualifiers, Kovačić made two more competitive appearances for Croatia, as Croatia scraped into the FIFA World Cup play-offs having taken only one point from their last four qualifiers. Although he did not participate in the scoreless first leg of the play-off against Iceland in Reykjavík, Kovačić started the second leg between the two teams in Zagreb, making an assist for the team's second goal as they reached the 2014 FIFA World Cup with a 2–0 win on aggregate.
On 2 June 2014, Kovačić was named as a member of Croatia's World Cup squad. He was in Croatia's starting team for the opening game of the tournament, a 3–1 defeat to World Cup hosts Brazil at the Arena Corinthians, São Paulo, where he played for his team for 60 minutes before being substituted. He went to play all the remaining games in the group stage, as Croatia was eliminated in the group stage. On 7 June 2015, he scored his first international goal in a 4–0 victory over Gibraltar, coming in his 20th appearance for the team.
On 4 June 2018, Kovačić was selected in Zlatko Dalić's 23-man squad for the 2018 FIFA World Cup. On 22 June, Kovačić provided an assist to his teammate Ivan Rakitić as he scored Croatia's third goal in a 3–0 win over Argentina in their second group stage match of the tournament. Croatia was beaten 4–2 by France in the final on 15 July.
Kovačić appeared in Croatia's 2018–19 UEFA Nations League A matches against Spain away and England home, that ended up as 6–0 defeat and a goalless draw, respectively. He featured throughout Croatia's successful Euro 2020 qualifying campaign, as they finished top of the group. In a 2–1 win over Wales in Osijek on 8 June 2019, he scored what would have been a goal for 2–0, however it was disallowed as Andrej Kramarić was in an offside position. In a return leg on 13 October, in the build-up to Wales' goal, Kovačić was controversially injured by Ben Davies as the match ended up as a 1–1 draw.
During Croatia's 2020–21 Nations League A campaign, Kovačić was heavily criticised for his inefficiency in the national team, especially after making an error that led to Dejan Kuluševski's opening goal in Croatia's crucial match against Sweden on 14 November 2020, that eventually finished as a 2–1 defeat. However, three days later, he scored two goals in a 3–2 defeat to Portugal, which eventually saved Croatia from relegation to the 2022–23 Nations League B as they achieved better goal difference than Sweden.
On 17 May 2021, Kovačić was selected in Dalić's 26-man squad for UEFA Euro 2020 and started all three group stage matches. In contrast to Croatia's Nations League campaign, his performances earned him widespread praise in the country as Croatia finished as the group runners-up and progressed to the round of 16. On 3 June 2022, in a 3–0 defeat to Austria in the 2022–23 Nations League A, Kovačić captained Croatia for the first time. At the 2022 FIFA World Cup, Kovačić received further praise for his performances as Croatia finished in third place.
On 20 May 2024, he was selected in the 26-man squad for the UEFA Euro 2024. A few weeks later, on 3 June, he earned his 100th international cap in a 3–0 friendly match win against North Macedonia prior to the tournament.
On 18 May 2026, Kovačić was selected in the 26-man squad for the 2026 FIFA World Cup.