The play occurred late in the second period of Winnipeg's 3-2 loss to New York on Tuesday night. Miller had fallen to the ice near the crease after taking a swipe at a rebound off the pads of Jets goalie Ondrej Pavelec.
Byfuglien drove his stick in to the back of the Rangers forward's head while falling to his knees. The league's video explanation of the suspension characterized the blow as ''dangerous'' and delivered with ''excessive force.''
Byfuglien will lose $111,827 in pay.
Winnipeg has lost its last two games and is two points ahead of Los Angeles in the race for the Western Conference's second wild-card spot. The Jets have five games remaining in the regular season, while the Kings have six.