Born in Stenlille, Nielsen won 2005 Individual Speedway FIM Youth Gold Trophy 80 cc, unofficial U-16 World Championship.
In 2011 he came to the UK to try to get a team place and got a place in the Workington Comets team towards the end of the season. In December 2011 he was announced as the final member of the 2012 Leicester Lions team in the British Premier League. After an injury early in the season, he showed good form before suffering a broken femur in a crash with team mate Jari Mäkinen on 23 June. Simon re-signed for Leicester Lions for the 2013 Premier League season. In May 2013 he was dropped by the Lions with his place going to Alex Edberg. In June he signed for Plymouth Devils. In 2014 he signed for Newcastle Diamonds, staying with the team for 2015.