The starting outside linebacker had been participating in optional workouts this month under an injury waiver. He fell to the turf Tuesday while backpedaling and grabbed the same knee in which he tore the anterior cruciate ligament in November.
Davis walked off the field, but didn't return to the practice. A team spokesman says Davis was undergoing tests and they could know more Wednesday.
Starting cornerback Richard Marshall also signed his one-year, $1.759 million tender on Tuesday.
The Panthers made no attempt to ink either player to a long-term deal.