During his active career, Mjelde spent two seasons at Austria Wien, two and a half seasons at Lillestrøm and a total of 7 seasons at Brann. He also played one season in Bryne – before he went to Lillestrøm. Towards the end of his career, he was loaned out to Sogndal in 2001. Mjelde scored 72 goals in 160 matches for Brann, earning himself and the team silver medals in 1997 and 2000, bronze medals and a cup silver as losing finalists in 1999 and an advancement to the quarter final in the Cup Winners' Cup in 1997, in which they were eliminated by Liverpool. After returning to Brann from Austria in 1996, Mjelde scored 19 goals in 15 league appearances, earning him the Kniksen award as "striker of the year". Mons Ivar played 3 games and scored 2 goals for Norway.
His first four years as a head coach saw Mjelde win both the league and the cup in Norway. Retiring as a player after the 2001 season, Mjelde became the new coach for Brann's reserve team in the Norwegian Second Division. The year after, Brann's head coach, Teitur Thordarson left the club. In January 2003, after only one year's experience as a coach, Mons Ivar Mjelde was appointed head coach in SK Brann. The season resulted in Brann finishing 6th, a major improvement from the previous year. The following year he guided Brann to a bronze medal in the premiership. They also won the cup, the first trophy in 22 years.
In the 2005 season, Brann finished 6th. 2006 was a better season for Mjelde and Brann, who finished as runners-up to Rosenborg. In 2007, his coaching career hit new heights as he took Brann to their first league title in 44 years, six points ahead of Stabæk. On 7 October 2008, Mons Ivar Mjelde announced that the 2008 season would conclude his spell in Brann.
Mjelde was officially appointed as head coach for Bryne on 1 June 2009. In 2011 he coached Valestrand Hjellvik for two games before being snapped up by Start. He was hired as head coach of Start half-way through the 2011 season, but could not save the team from relegation. The next season, Start won the Adeccoligaen and consequently promotion to the Norwegian Premier League in the 2012 season.