The league sanctioned Brown for delivering an elbow to the face of Minnesota's Jason Pominville during the Kings' 2-1 loss Tuesday to the Wild.
Pominville fell and was dazed as he left the ice after the hit in the second period and didn't return to the game. No penalty was called.
The Minnesota forward was listed as day-to-day with an upper body injury.
NHL discipline czar Brendan Shanahan said the suspension was warranted because the blow was purposeful and not caused by any movement by Pominville.
Brown will miss the Kings' final regular-season games against Detroit and San Jose.
Defending NHL champion Los Angeles will begin the playoffs next week as the fourth seed in the Western Conference.