Matthews, who ranks fourth in the NFL with nine sacks, injured his hamstring 10 days ago in Green Bay's win over the Arizona Cardinals. The Packers had a bye this past weekend, but it didn't offer enough time for Matthews to recover.
"I know Clay's not going to be available this week, and we'll see what next week brings us," coach Mike McCarthy said at his Wednesday afternoon press conference. "He was diagnosed as being a couple weeks away, and this will be his second week. We'll see what happens next week.
"We've been planning to play this week without Clay Matthews."
Matthews, 26, has battled hamstring injuries throughout most of his four-year NFL career, but the injury has kept him out of only one game prior to this.
Green Bay's other starting outside linebacker, rookie first-round pick
Nick Perry, was placed on injured reserve last week. The Packers' defense will now rely on Erik Walden — who started 15 games last season — on one side and either undrafted rookie Dezman Moses or third-year linebacker Frank Zombo on the other. Zombo was recently activated from the Physically Unable to Perform list. The Packers are also without starting inside linebacker Desmond Bishop (hamstring) and his backup, D.J. Smith (knee), for the rest of the season.
"Any time a player like Clay is not able to play, I think everybody on the defense has to pick up their level of play," Walden said. "Me and Moses and Zombo, we're going to mix it up. Just try to keep them off-balance.
"Everybody in that room can play. Any time you're in that defensive room, you're counted on to step up."
Matthews joins a growing list of injured star players on Green Bay's sideline, including wide receiver Greg Jennings (abdominal surgery) and defensive back Charles Woodson (broken collarbone), both of whom were also ruled out on Wednesday for Sunday's game. Starting right tackle
Bryan Bulaga (hip) was ruled out for the season earlier this week.
"I had a chance to watch Charles Woodson work out yesterday in the weight room," McCarthy said. "I think he's a lot closer than any of us thought he would be at this time. Same with Greg Jennings. His workouts are going very well."
Jordy Nelson (hamstring/foot) was limited in Wednesday's practice. He initially injured his hamstring in practice three weeks ago and, after missing one game, returned for the next game before then injuring his ankle and foot in the first quarter.
"I thought Jordy Nelson looked his old self," McCarthy said. "I don't have a very high, or any level of concern. I thought he practiced well. He looked normal."