Born in Næstved, Makienok began his professional career at Herfølge Boldklub, which later became HB Køge, making his debut in 2009, before joining Brøndby IF in January 2012 for a fee of €550,000.

[2] Makienok grew up in Herlufmagle, and started playing for local club Suså IF at the age of 4, before making the move to Næstved Boldklub a few years later.

[4] He later told in the radio-show Fodboldeffekten on Radio 100, that Næstved Boldklub tried to retain him by offering him a job in a local Shell fuel station, due to lacking funds to pay players.

[9] Makienok joined Brøndby IF on 28 January 2012 on a €550,000 transfer from HB Køge, signing a four-year contract which tied him to the club until the summer of 2016.

[15] In the same year, he caught the attention of several French clubs[16] and English sides Crystal Palace[17] and Fulham while his price tag was reported as over €4 million.

[18] According to several Danish media sources, Makienok had rejected a contract extension wanting to pursue new challenges during the 2014 summer transfer window.

Several Serie A clubs revealed their interest, with Palermo leading Atalanta, Cesena and Scottish side Celtic in the chase, as his price tag was now €3 million according to Danish media.

[29] On 7 June 2017, Makienok signed a three-year contract with Dutch Eredivisie club FC Utrecht, where he was meant to succeed Sébastien Haller as the team's target-man.

[30][31] After making two appearances in the Europa League qualifiers he tore his anterior cruciate ligament keeping him sidelined for a lengthy period.

[32][33] Makienok had multiple complications and setbacks during his rehabilitation, only making his comeback on the pitch two years after suffering the injury, on 31 October 2019 in a 4–1 cup win over fifth tier club Excelsior '31, in which he scored a goal.

[34][35] A few days later, on 3 November, he was subbed on against Fortuna Sittard in the Eredivisie and scored his first goal in the Dutch league only three minutes later as Utrecht won 6–0.

[43] He was declared healthy again on 23 May,[44] and made his return to the pitch for Dresden on 9 June in a 1–1 home draw against Greuther Fürth, where he scored the equaliser after coming on for Jannik Müller during the half.