Micic was born in Stockholm to a Serbian father and a Croatian mother. He began playing basketball at the age of 6, and by the time he was 10, he was already playing for the youth teams of Södertälje Kings.
Micic made his professional debut for Södertälje Kings in 2007, at the age of 17. He quickly established himself as one of the team's best players, and in 2009, he was named the Swedish Basketball League's Rookie of the Year.
After three seasons with Södertälje Kings, Micic moved to Spain, where he played for Unicaja Málaga for two seasons. He then spent one season with Red Star Belgrade in Serbia, before returning to Unicaja Málaga in 2014.
In 2016, Micic signed a two-year contract with the Utah Jazz of the National Basketball Association (NBA). He made his NBA debut on October 22, 2016, against the Sacramento Kings. He was waived by the Jazz on December 26, 2016, after appearing in 20 games.
After his release from the Jazz, Micic returned to Europe, where he signed with Žalgiris Kaunas of the Lithuanian Basketball League (LKL). He spent two seasons with Žalgiris Kaunas, and he helped the team win the LKL championship in 2018.
In 2020, Micic signed a three-year contract with Anadolu Efes of the Turkish Basketball Super League (BSL). He has been named the BSL MVP in both of his seasons with the team, and he has also helped Anadolu Efes win two BSL championships and two EuroLeague championships.
Micic has represented Sweden at the international level since 2009. He has played for the Swedish national team at the EuroBasket tournament in 2013, 2017, and 2022.
Micic is married to Jelena Micic, and they have two children together. He is also an active philanthropist, and he has donated money to various charities, including the Serbian Red Cross and the Children's Cancer Fund of Croatia.