Skinner, the league's youngest player at 18, leads all rookies with 40 points and 22 assists while ranking second with 18 goals.
Stastny will be making his first appearance at the All-Star Game. He was selected in 2008 but was injured and didn't play.
Stastny's father, Peter, played in six NHL All-Star games during his 15-year career from 1980 to 1995. The Stastnys will become the eighth father-son tandem in NHL history to play in the All-Star Game.
Stastny has 42 points in 47 games. His teammate, Matt Duchene, also will play.