Byrd, who in March signed a deal reportedly worth $54 million with $28 million in guaranteed money, also underwent back surgery in the offseason. Over four games this season, Byrd has recorded 17 tackles and two passes defended. Veteran Rafael Bush is expected to take Byrd's place in the starting lineup.
Byrd, 27, joined the Saints after spending the first five seasons of his career with the Buffalo Bills.
The Saints, who rank 28th in the NFL in passing yards allowed per game (272.5), are 1-3 this season with a win over the Minnesota Vikings and losses to the Atlanta Falcons, Cleveland Browns and Dallas Cowboys.
New Orleans hosts the Tampa Bay Buccaneers (1-3) on Sunday.
- Chris Johnson