Skjei notched a power-play assist and two shots on goal in Saturday's 4-1 win over the Jets.
Skjei produced an assist, four shots on goal, four PIM and a plus-3 rating in Tuesday's 4-0 win over the Bruins.
Skjei scored his first goal of the season in Tuesday's 7-3 defeat to Seattle.
Skjei agreed to terms on a seven-year, $49 million contract with Nashville on Monday, Elliotte Friedman of Sportsnet reports.
Skjei collected an assist in Thursday's 3-2 overtime loss against the Rangers in Game 3.
Skjei recorded two assists in a 6-3 victory over the Islanders in Game 5 on Tuesday.
Skjei (rest) was back at practice Thursday after getting Tuesday's game versus Columbus off, Walt Ruff of the Hurricanes' official site reports.
Skjei (rest) will be out of the lineup Tuesday versus the Blue Jackets, Walt Ruff of the Hurricanes' official site reports.
Skjei (rest) will be in the lineup Tuesday versus the Blue Jackets, according to Walt Ruff of the Hurricanes' official site.
Skjei will not play Sunday against Chicago, Walt Ruff of the Hurricanes' official site reports.