Skjei represents the United States in international play. His first taste of international hockey was at the 2011 World U-17 Hockey Challenge, where he recorded one goal and three assists in 6 games, while helping the USA to a second-place finish. In 2012, Skjei played in several tournaments with the American Under-18 team, including the 2012 IIHF World U18 Championships, capturing a gold medal in the first International Ice Hockey Federation sanctioned tournament he played in. He attended the American evaluation camp in preparation for the 2013 World Junior Championship, but was not selected for the final team. Skjei was selected to the American team for the 2014 World Junior Tournament,