There is no exact timetable for Addison's return from Birmingham, but team officials are optimistic the outside linebacker will play in Sunday's game against the Tennessee Titans.
On Monday, Addison posted to Instagram a picture of him and his brother, Gjamal Antonio Rodriqcus, with the words: "This pain is real. Half of my soul gone wen u killed my baby brother last nite. Please live through me n Rest well lil bruh."
Carolina coach Ron Rivera said he has kept in touch with Addison the past few days and given him "positive messages of support."
"He's been a big part of what we've done and the success we've had and the success we're having," said Rivera, whose 4-3 team had won four straight prior to Sunday's loss at San Francisco. "He's most certainly missed and we most certainly do think about him and pray for his family."
The shooting happened at 7:15 p.m. in Birmingham. Police found Rodriqcus and a woman inside a vehicle; both suffered from gunshot wounds. Rodriqcus, 27, was pronounced dead at the hospital.
Suspect Darius Frazier, 22, reportedly has been charged with capital murder in Rodriqcus' death and attempted murder for the shooting of the woman.
Addison ranks 11th in the NFL in sacks this season with 6.5.