Šarić began his basketball career at the Dražen Petrović Basketball School in Croatia and made his first professional appearance with KK Zrinjevac in 2009–10. He moved to KK Zagreb in December 2009 and signed with Dubrava Zagreb for the 2010–11 season. Returning to KK Zagreb in 2011–12, Šarić then spent two seasons with Cibona Zagreb before transferring to Anadolu Efes at the start of the 2014–15 season. After two seasons with our club he moved to the NBA, where he has played for the Philadelphia 76ers, Minnesota Timberwolves, Phoenix Suns, Oklahoma City Thunder, Golden State Warriors, Denver Nuggets and Sacramento Kings.

Šarić was the MVP of the 2010 FIBA Europe U16 Championship, where Croatia won gold. He helped the Croatian junior national team claim the 2012 FIBA Europe U18 Championship, averaging 25.6 points per game and earning tournament MVP honors.

With Cibona Zagreb in 2012–13, Šarić won the Croatian League and Croatian Cup and played a key role in his team’s Adriatic League title, being named Finals MVP. He was also voted FIBA Europe’s “Young Player of the Year” in 2013 and 2014.

Wearing the Anadolu Efes jersey in 2014–15, Šarić won the Turkish Cup and Presidential Cup. In November 2014 he was named EuroLeague MVP of the Month, becoming the youngest player to receive the award at that time.