Career
Nielsen began his career with KB, before joined Chelsea"s academy in 2005 and became a pro in July 2007. He has made several appearances for the Danish Under 18 national football team On 31 March 2009, whilst being tracked by many European clubs as Rennes, Saint Etienne, Brøndby and Celtic, Nielsen joined Superettan team Landskrona BoIS on loan until the end of the season.
On 9 July 2009, Nielsen ended his contract with Chelsea on a mutual agreement, becoming a free agent, and on 21 July 2009 joined Arizona Alkmaar on a free transfer after impressing in a trial.
On 13 March 2010, it was announced that he would return to Landskrona BoIS on loan. In the summer of 2010, he went back to Denmark to play for Football Club Midtjylland.
In January 2012, he went to play for Greve Fodbold in the Danish fourth tier. The club was at that time managed by his father Benny Nielsen.
In January 2015, he was signed by Sligo Rovers ahead of the 2015 League of Ireland season.
Morten is the son of the former professional Danish football player Benny Nielsen, who now works as an agent.