[8] Born in Kokkedal, Mørkøv started as a track cyclist, becoming national champion in the points race in 2004.

Mørkøv rode his first Tour de France in 2012, drawing attention by featuring in the most important escapes of the first three stages, where he gained enough points to lead the mountains classification.

[10] Mørkøv joined the Belgian Quick Step team in 2018 and since then has acted as a successful lead-out man for Sam Bennett and then, as a late replacement for Bennett as the team's sprinter for the 2021 Tour de France, Mark Cavendish.

[11] Mørkøv has been highly praised; Cavendish said “It’s a known fact Michael is the best leadout man in the world"[11] and retired sprinter Marcel Kittel said "Many sprinters would win with him as the last man on the sprint train".

[11] In 2021 when the Madison track race was reinstated into the Olympic Games of Tokyo 2020, Mørkøv won the gold medal (partnered with Lasse Norman Hansen)