A highly touted prospect[citation needed] while in high school, Nielsen was drafted by the New York Rangers in the fourth round, 69th overall in the 1990 NHL Entry Draft. After being drafted, Nielsen choose to play in the college ranks and played for the University of Minnesota for four years. He gradually improved each year and led the team in points during his senior season (1993–94) and earned a spot on the WCHA second All-Star team the same season.\n', '

After college Nielsen joined the Rangers minor league affiliate Binghamton Rangers. He played three years with Binghamton, most notably scoring 53 points in 76 games during the 1996–97 season. That year he also made his NHL debut, appearing in two games with the New York Rangers.\n', '

Nielsen then signed with the Mighty Ducks of Anaheim. He split the 1997–98 season between the Mighty Ducks and their minor league affiliate Cincinnati Mighty Ducks. For the 1998–99 season Nielsen was able to crack the Anaheim starting lineup, playing 80 games and scoring 9 points. The 1999–2000 season saw Nielsen play in 79 games and score an NHL career high 18 points.\n', '

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