Micov played for youth teams of Beopetrol and Crvena zvezda before turning pro in 2003. Micov began his pro career in the 2003–04 season with OKK Beograd. He then moved to Lavovi 063 in the 2004–05 season. He joined Budućnost Podgorica for the 2005–06 season. He moved to Partizan Belgrade in 2007. He won the Serbian League championship with Partizan Belgrade in 2007. He then returned to Budućnost Podgorica for the 2007–08 season.
In July 2012, he signed a one-year deal, with an option for a second year, with the Russian team PBC CSKA Moscow. In June 2013, CSKA decided not to use the out option on his contract, and thus kept him in the club for one more season. In July 2014, his contract with CSKA expired, and he became a free agent.
Galatasaray (2014–2017)
On July 14, 2014, he signed with the Turkish team Galatasaray Liv Hospital. On June 15, 2015, he signed a two-year contract extension with the club. In the 2015–16 Eurocup season, he was named to the All-EuroCup First Team. Galatasaray then won the EuroCup championship, later that same season.
Olimpia Milano (2017–present)
On July 10, 2017, Micov signed with Italian club Olimpia Milano. In 2017–18 LBA season, Olimpia Milano won the championship after 4–2 record in the 2018 LBA Finals over Trento. Over 26 league games, Micov averaged 11.7 points and 3.2 rebounds, while shooting 45.8% from the field. In 2017–18 EuroLeague season, he averaged 10.9 points and 2.6 rebounds over 29 games. On September 30, 2018, Micov was named MVP of the 2018 Italian Supercup. In 2018–19 season, Olimpia Milano secured the first position in the regular season of Italian League, but was stopped with 3–0 in the semifinal series by Dinamo Sassari. Micov averaged 9.7 points, 2.7 rebounds and 2 assists over 32 games of the Italian League. In 2018–19 EuroLeague, he averaged 13.9 points, 3.2 rebounds and 2.5 assists over 30 games. On July 2, 2019, Micov signed a two-year contract extension with Olimpia Milano.
Micov won the gold medal at the 2001 FIBA Europe Under-16 Championship as a member of the FR Yugoslavia youth national team. He won the bronze medal at the 2005 FIBA Europe Under-20 Championship, as a member of the Serbia and Montenegro junior national team. His breakthrough in the senior Serbian national team was set back by injuries, but he was eventually a part of the preliminary Serbia national squad during training camp for the 2014 FIBA Basketball World Cup. The then 29-year-old was widely expected to make the team's final roster cut, however, during the last preparation friendly game, against New Zealand, Micov got into a mid-game argument with Serbian head coachAleksandar Đorđević, that led to Đorđević taking Micov out of the game, and later expelling him from the bench. At the post-game press conference, the Serbian coach announced that, "Micov's short career in the national squad has ended", with Micov later saying to the media that he read the coach's words, and that he accepted his decision, while also stating that Đorđević was, "maybe too nervous".
