Packers coach Mike McCarthy on Monday called the injury "significant" and said it required him to stay overnight in Washington for a procedure so he can travel back to Green Bay.
"I would say it's significant but that's as far as the details I have right now," he said.
Wilkerson got leg-whipped by Packers safety Kentrell Brice late in the second quarter of the Packers' 31-17 loss to the Washington Redskins. Brice immediately motioned to the Packers' bench for medical assistance and Wilkerson was carted off the field.
Wilkerson, 28, was one of the Packers' marquee free-agent signings this offseason. First-year general manager Brian Gutekunst gave the former New York Jet a one-year, $5 million contract to try to resurrect his career in Green Bay. The deal also contained up to $3 million in incentives.
The Jets cut Wilkerson this offseason after just two seasons of a five-year, $86 million contract.
Wilkerson had quickly grown close to the Packers' defensive linemen, especially fellow New Jersey native Mike Daniels, who did not want to have leave Wilkerson behind in the Washington area Sunday night.
"He sits right next to me on the friggin' plane," Daniels said Monday. "I'm like, fudge. It's just all bad. But now it's back to the original four."
The Packers almost certainly will add a defensive lineman when they place Wilkerson on injured reserve, but for now it's Daniels, Kenny Clark, Dean Lowry and Montravius Adams at the position. They have two rookie defensive linemen on the practice squad: seventh-round pick James Looney and undrafted free agent Tyler Lancaster.
But Clark and Daniels are back to being the leaders of the group. Clark, the Packers' 2016 first-round pick, finished last season strong with 4.5 sacks in his final five games. He played 56 of the 61 defensive snaps against the Redskins, while Daniels played 49, Lowry 24 and Adams five.
"I did it before," Clark said of having to play more snaps. "I can. If that's what's asked of me, I can. I'm not going to ever say no. If I had the choice, I'd be out there every play if I could. I can, if that's what needed."
McCarthy also said right tackle Bryan Bulaga (back) and right guard Justin McCray (shoulder) were still undergoing tests, and he could not say whether they would be available Sunday against the Bills.
Linebacker Nick Perry is in the concussion protocol, McCarthy said. Perry had seven tackles in the Packers' loss Sunday.