Brown was hurt during the Saints' 29-25 victory over Atlanta last Sunday.
The injury was not deemed serious, but still bothered him enough to keep him out of action in a short week for New Orleans (7-6).
Zach Strief is slated to start in Brown's place, as he has once in each of the previous two seasons.
Brown was drafted 13th overall by the Saints in 2005 and won the starting job his rookie season before getting a Pro Bowl nod following the 2006 season.
Meanwhile, running back Deuce McAllister missed practice because of a death in the family. His status for Thursday night's game was not immediately clear. Lately, he has played a limited role behind running backs Reggie Bush and Pierre Thomas.
Starting defensive end Will Smith, who missed Tuesday's practice for the birth of his son, returned Wednesday.
La Liga Team Of The Week: Round 6
Vikings likely won’t have LB Henderson vs. Saints
