Byfuglien will lose $111,827 in pay and be eligible to play in the team's final game of the season. Winnipeg is currently two points ahead of the Los Angeles Kings, who have six games left, for the second wild-card spot in the Western Conference.
The cross-checking penalty came 17:20 into the second period of the Jets' 3-2 loss to the Rangers on Tuesday. Miller fell to the ice after leaping out of the way of a shot and then trying to slap at the rebound when the puck was blocked by Jets goalie Ondrej Pavelec.
Byfuglien then delivered a blow with his stick to the back of the head of Miller, who was lying on the ice, in a manner the league described as "excessive" and "dangerous." No penalty was called on the play, though.
Rangers Coach Alan Vigneault was extremely critical of the cross-check after the game.
"Violent, deliberate," Vigneault told reporters Tuesday. "Could have broken his neck. It was one of the most vicious cross-checks I’ve seen this year."