Skjei played two seasons of high school hockey in Minnesota for the Lakeville North Panthers. In his first season with the team, he was named Rookie of the Year, and in his second he was named the team's Most Valuable Player. For his final two years of high school, Skjei played with the USA Hockey National Team Development Program, based out of Michigan. He spent one season with the Under-17 team, and one with the Under-18 team. After his final season with the National Team Development Program, Skjei was selected by the New York Rangers in the first round of the 2012 NHL Entry Draft. During his freshman season at the University of Minnesota, Skjei played in 36 games, recording one goal and two assists.
Professional
New York Rangers
Skjei signed a contract with the New York Rangers on April 1, 2015. He reported to the Hartford Wolf Pack of the AHL as an Amateur Tryout to finish the 2014–15 season. Skjei scored his first professional goal in a Calder Cup playoff game against the Providence Bruins on April 26, 2015. He was promoted to the Rangers from Hartford on December 15, 2015 after recording 2 goals and 9 assists in 27 games for the Wolf Pack to start the 2015–16 season. Injuries to various New York Rangers' defenseman increased Skjei's ice time, but he failed to score any points in the 7 regular season games he played for the team. In the playoffs, Skjei recorded two assists as the Rangers were eliminated in the first round in 5 games by the Pittsburgh Penguins. On December 11, 2016 Skjei scored his first NHL goal against the New Jersey Devils. On April 16, 2017 he scored his first career playoff goal against the Montreal Canadiens. On April 29, 2017, Skjei had his first multiple goal game, when he scored two goals against the Ottawa Senators in the 2017 Stanley Cup playoffs. On June 21, 2017, Skjei was named to the NHL's 2017 All-Rookie team. Returning for his sophomore 2017–18 season, the Rangers struggled as a team, announcing a team rebuild in February. Skjei would see his points total dip to 25, but also a significant increase in ice time following the trade of team captainRyan McDonagh. After his second season, Skjei signed a six-year deal with the Rangers on July 28, 2018.
Carolina Hurricanes
On February 24, 2020, Skjei was traded to the Carolina Hurricanes in exchange for a 2020 first-round pick.
While attending Lakeville North High School in Minnesota, Skjei played quarterback on the varsity football team and was also a member of the golf team. His grandfather played football at the University of Minnesota.
In popular culture
Skjei was portrayed by Alex Moffatt in the November 18, 2017 episode of Saturday Night Live, hosted by Chance the Rapper. Skjei was reported to have enjoyed the sketch, which poked fun at the pronunciation of his surname.
