Biković initially gained recognition for his roles in Sunstroke (directed by Oscar-winning director Nikita Mikhalkov), Dukhless 2, and Beyond the Edge.

After his parents' divorce, which occurred when Miloš was very young, his father moved to Germany and Biković was left to live with his mother in Serbia.

[7][8][9] Biković made his acting debut on television, in the popular RTS series The Dollars Are Coming (Serbian Cyrillic: Стижу долари).

In 2010, Biković was cast to portray Serbian footballer Aleksandar "Tirke" Tirnanić in Montevideo, God Bless You!

Directed by Dragan Bjelogrlić, it is the true story of the Yugoslavia national football team qualifying for the 1930 FIFA World Cup.

[14] The television series adapted from Montevideo, God Bless You!, which features some scenes and characters that do not appear in the original film, premiered on the RTS on 13 February 2012.

He also made his stage debut in the Atelje 212 production Goodbye SFRY (Zbogom SFRJ), inspired by Wolfgang Becker's film Good Bye, Lenin!

[16] In 2012, Biković portrayed Serbian scientist Mihailo Petrović Alas in Professor Kosta Vujic's Hat (Šešir profesora Koste Vujića), a film adaptation of the novel of the same name by Milovan Vitezović directed by Zdravko Šotra.

[18] In 2013, Biković starred the RTS series Ravna Gora that takes place in Yugoslavia during World War II and tells the story of the Chetnik resistance movement,[19] the National Theatre production of The Lady of the Camellias,[20] and the German independent short film Great.

Role of Pavel in series Hotel Eleon brought him a status of star in Russia, Kazakhstan, Azerbaijan and rest of the former USSR countries.

[30] In 2018, Biković appeared in the leading role of the movie The South Wind, directed by Miloš Avramović, which earned a record number of unique views.

A Russian-Serbian action movie, directed by Andrei Vologin, is dedicated to the secret operation to take over Slatina airport in Kosovo and Metohija during the 1999 NATO bombing in FR Yugoslavia.

In 2020, Biković starred in the Russian-Serbian romantic comedy Hotel Belgrade alongside Jakov Jevtović and Miodrag Radonjić.

[42] In 2016, he founded a production company Archangel studios and produced 4 projects South Wind, The Balkan Line, Embasy, and Hotel Belgrade.