Quick has a lower-body injury, the Kings said Saturday, and there is no timetable for his return. The injury is not believed to be related to the lower-body injury Quick sustained in practice Oct. 6 that led to him missing five games.
Jack Campbell will start against the Rangers.
Brown, a forward, broke a finger during Los Angeles' preseason finale Sept. 29.
The Kings have been outscored 29-8 during the streak and have lost all six games in regulation. A loss would give them their longest losing streak since they dropped eight in a row (0-8-0) from Dec. 12-26, 2007.
The Rangers opened a four-game road trip with a 4-1 loss to the Chicago Blackhawks on Thursday. New York is 0-3-1 on the road this season.