Skjei became a part of the Nashville Predators' splash in free agency for the 2024-25 season when the defenseman signed a seven-year, $49 million contract July 1, 2024, joining forwards Steven Stamkos and Jonathan Marchessault.

He established himself during five seasons with the Carolina Hurricanes that followed five with the New York Rangers, who chose him in the first round (No. 28) of the 2012 NHL Draft. Skjei's nine points (one goal, eight assists) helped the Hurricanes reach the Eastern Conference Second Round of the 2025 Stanley Cup Playoffs, a six-game loss to the Rangers. During the regular season, Skjei was one of eight defensemen to score at least one power-play goal and one short-handed goal.

A product of USA Hockey's National Team Development Program, Skjei played for the University of Minnesota for three years. He made his NHL debut against the Edmonton Oilers on Dec. 15, 2015, had 39 points (five goals, 34 assists) in 2016-17 and helped the Rangers reach the second round with four goals in 12 playoff games.

Skjei was traded to the Hurricanes on Feb. 24, 2020 for a first-round pick at the 2020 NHL Draft.