He suffered the injury when he was hit by a shot on the power play from center Anze Kopitar in a 3-0 loss to the Anaheim Ducks.
Brown, 33, was the Kings' second-leading scorer last season with a career-high 61 points. He skates on the top line with Kopitar and Alex Iafallo.
He has been an iron man for the Kings, missing only 18 regular-season games since he became a starter in the 2005-06 season. He has played his entire career with the team.
The Kings' regular season opens Friday with a home game against the San Jose Sharks.