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 in the 2010 Entry Draft.
Collegiate
Nelson competed with the University of North Dakota Fighting Hawks for two seasons while majoring in pre-investments. He recorded his first collegiate goal on a power play to lift the Hawks 3–2 over Minnesota Duluth. Later in the season, he recorded his first two-goal game in a win over Robert Morris Colonials. He recorded a goal off an assist from Joe Gleason to help lead the Fighting Hawks to the WCHA Final Five. Nelson ended the season with the Tom Hoghaug Memorial Scholarship as he led all Sioux freshmen in points and goals. He was also named to the All-WCHA Team and WCHA All-Tournament Team. In his sophomore season, Nelson played on a line with Corban Knight and Danny Kristo. By the conclusion of the 2011–12 season, Nelson was named to the All-WCHA Third Team after leading all WCHA players with 20 goals and becoming UND's youngest 20 goal scorer since Jonathan Toews. He was also named a Inside College Hockey All-American, to College Hockey NewsSecond Team, and Inside College Hockey's WCHA Breakthrough Player of the Year. Nelson ended his collegiate career by signing an Entry Level Contract with the New York Islanders on April 3, 2012.
Professional career
Nelson began his professional career with the Islanders' minor league affiliate, the American Hockey League's Bridgeport Sound Tigers after the 2011–12 season, during the 2012 Calder Cup playoffs. He eventually made his NHL debut during the 2013 Stanley Cup playoffs with the Islanders after the 2012–13 regular season. He registered his first NHL point the following season on October 8, 2013, an assist on a goal by Peter Regin in a 6–1 win against the Phoenix Coyotes. His first NHL goal was scored on October 22, 2013 against Roberto Luongo of the Vancouver Canucks. On October 9, 2017, St. Louis Blues enforcer Robert Bortuzzo cross-checked Brock Nelson multiple times while he was down after Nelson collided with a teammate. Bortuzzo was later fined $3,091.40. On May 23, 2019, after a career year in the 2018–19 season with 53 points under Barry Trotz, Nelson signed a six-year, $36 million contract to remain with the Islanders.