He was injured in Sunday's victory over the Jacksonville Jaguars.
Werner, who was picked in the first round (24th overall) of April's draft and is mainly used in nickel packages, has five tackles and half a sack this season.
"He was getting comfortable," coach Chuck Pagano said about Werner. "You could see the confidence level rising. He was playing faster. It's a shame it happened, but it's part of the game."
Pagano didn't have an update on running back Ahmad Bradshaw, who missed Sunday's game with a neck injury.
Safety LaRon Landry's status for this week's game against undefeated Seattle is "still up in the air." Landry has missed the past two games with an ankle injury.