Finley said his knee isn't a major concern, but he seemed to agree it might be smart for him to sit out Sunday's game.
"Would it be smart? Of course it would be smart; everybody thinks that," Finley said, according to the Green Bay Press-Gazette. "But I ain't the head coach or the GM, so I'm going to leave that up to them."
The news of Finley's injury comes as McCarthy is weighing the possibility of resting veteran players Sunday, given the Packers already have clinched the No. 1 seed in the NFC.
Defensive end Ryan Pickett returned to practice Wednesday for the first time since he sustained a concussion during the Packers' Dec. 11 victory over the Oakland Raiders. It was Pickett's second concussion this season.
Left tackle Chad Clifton (hamstring) also practiced, and McCarthy added that a determination on the lineman's status would be made after he made it through Thursday's padded practice.
Wide receivers Greg Jennings (knee) and Randall Cobb (groin), running back James Starks (knee) and right tackle Bryan Bulaga (knee) didn't practice Wednesday. McCarthy said Jennings still isn't ready to play this week but is getting close, as is Bulaga, whom the coach hopes will practice Friday.
The Associated Press contributed to this report.