Nelson played hockey at Warroad High School, where he was a finalist for the Minnesota Mr. Hockey Award, given to the top Minnesota high school hockey player. He finished the 2009–10 season with 39 goals and 34 assists for 73 points in 25 games for Warroad. On September 24, 2009, Nelson committed to play Division 1 hockey for the University of North Dakota after considering Bemidji State and Nebraska-Omaha and later partook in the 2010 USA Hockey National Junior Evaluation Camp. Nelson was selected 30th overall by the New York Islanders of the National Hockey League (NHL) in the 2010 Entry Draft.