Milošević began his career playing for Rissne IF and later transferred to Vasalunds IF. Operating as a striker till the age of 17, at Vasalund he first switched position to the central midfield and was then persuaded to move back to the central defense where he flourished. During the 2010 season he scored five times for Vasalunds IF, one from a penalty kick.
On the first of February 2011 he signed a four-year contract with his boyhood favourites AIK after a long and drawn out process that included training with AIK rivals Djurgårdens IF. He has also trained with Scottish club Celtic and Serie A club Fiorentina.
When AIK defender Per Karlsson was injured during pre-season training, Milošević was selected to play from start in the first home game of the 2011 season against Mjällby. AIK won the match and Milošević received a lot of attention, not only for being named man of the match, but also for receiving a martial arts inspired kick to the head from Mjällbys Peter Gitselov. During a home game against Malmö FF on 12 June, he provided his first assist for the club.
Liverpool, Arsenal, Spurs and Sunderland all had scouts keeping a very close eye on the young defender. Serbian club FK Partizan and several Dutch clubs, including Ajax have also shown an interest. Bundesliga club Werder Bremen made an official bid for 600,000 euros, a bid that AIK turned down. His agent said that it would be good if the young player stayed with AIK for at least a year before moving on to a bigger club, but adds that if a good deal is offered, it is hard to turn it down.
He made his first goal in a home draw against GIF Sundsvall on 22 April 2012.
On 7 January 2015 Milošević signed a 3.5-year (with option to extend 2 more years) deal with Turkish club Beşiktaş for a fee of €1 million.
He was loaned to German Bundesliga side Hannover 96 on 1 February 2016 for the remainder of the season.
On 17 August 2016, Milošević signed a season-long loan deal with Bundesliga side SV Darmstadt 98. He said: "Everybody who has played in the Bundesliga wants to stay there."
Alexander’s father Goran immigrated from Serbia and his mother is Swedish with Finnish roots. Milošević played five games with the Serbian U17 team. In 2011, he accepted the Sweden U19 youth coach Hans Lindbom's invitation to a Sweden U19 training camp and soon received his first cap for both Sweden U19 and U21 squads.
Erik Hamrén, the senior manager of the Swedish national football team said at a press conference in January that Milošević would have been part of the senior squad that were to play friendlies with Qatar and Bahrain, had it not been for a broken foot.BeşiktaşSüper Lig: 2015–16Sweden U21UEFA European Under-21 Championship: 2015Allsvenskan Award for Best Newcomer: 2011