Žižić's first team was KK Split, in the 2013–14 season, but he played for their junior team, in which he only played in 3 games. He then moved to the Cedevita Zagreb's junior team, and with them he played in 5 games. To start the 2014–15 season, he played for Gorica. He moved to Cibona Zagreb for the rest of the season. In that year, he averaged 7.4 points, 0.3 assists, 0.3 steals, and 0.9 blocks, in 15.5 minutes per game, in 25 games played in the Adriatic League. His breakout season was in the 2015–16 season. He was named the 2015–16 ABA League season's Top Prospect. In that season, he averaged 12.7 points, 7.2 rebounds, and 1.2 blocks in 24.8 minutes per game, in 26 games played in the Adriatic League. He was also named to the European-wide 3rd-tier levelFIBA Europe Cup's Starting Five Team of the 2015–16 season. On 11 October 2016, Žižić was named the MVP of the fourth week of the 2016–17 ABA League season. After he scored 37 points and grabbed 20 rebounds, in Cibona's win against MZT Skopje Aerodrom, by the final score of 89–85, in a game that was decided after two overtimes. On December 27, 2016, Žižić left Cibona, and signed with the Turkish team Darüşşafaka Doğuş, of the Turkish Super League. With Darüşşafaka, Žižić made his debut in the European top-tier level, the EuroLeague, on 30 December 2016, in an 81–77 road loss against FC Barcelona. In his first EuroLeague game, Žižić had 4 points, 6 rebounds, 2 steals, and 2 blocks.
NBA
Žižić was selected with the 23rd overall pick in the 2016 NBA draft, by the Boston Celtics. On 1 July 2017, Žižić signed with the Boston Celtics. Before even suiting up for a single regular season game for the Celtics, Žižić was traded to the Cleveland Cavaliers alongside Isaiah Thomas, Jae Crowder, and the Brooklyn Nets' unprotected 2018 first round pick for Kyrie Irving on August 22, 2017. However, eight days after the trade was first confirmed, the Celtics would also add a 2020 second round pick from the Miami Heat in order to fully complete the deal to satisfy Cleveland's worries involving Isaiah Thomas' hip injury. Žižić has been going back and forth from Cleveland to Canton many times throughout his rookie season, mainly because he doesn't see much regular playing time with the Cleveland. However, after the All-Star break of 2018, he started seeing more minutes, primarily due to injuries of Kevin Love and Tristan Thompson. His best game of the period came on March 11, when he scored 15 points and had 7 rebounds in a loss to Los Angeles Lakers. In the last game of the regular season, however, he improved on that by scoring 20 points and grabbing 7 rebounds again. The Cavaliers made it to the 2018 NBA Finals, but lost the series 4-0 to the Golden State Warriors.
Žižić's older brother, Andrija, was also a professional basketball player. The two brothers were teammates at Cibona Zagreb, in the 2015–16 season. His older brother played in 107 EuroLeague games, with Cibona Zagreb, FC Barcelona, Olympiacos, and Panathinaikos, and he also won a EuroLeague championship with Maccabi Tel Aviv.
