The suspension came the day after Babchuk was sent down and the Hurricanes activated defenceman Frantisek Kaberle from the non-roster injured list.
Babchuk had two goals and 12 assists in 51 games with the Hurricanes.
Kaberle missed 55 games while he recovered from off-season shoulder surgery. He scored the decisive goal in Game 7 of last season's Stanley Cup final against the Edmonton Oilers.
He picked up where he left off Tuesday night, scoring the game-winning goal in his first game back, a 2-1 victory over the Montreal Canadiens.