Addison was ruled out on Saturday, the day after he laid to rest Gjamal Antonio Rodriqcus, who was shot to death last Sunday in Birmingham, Alabama.
Addison has been in his hometown all week. General manager Marty Hurney and Mark Carrier, the executive director of the Panthers' football staff, went to Birmingham on Friday for the funeral and to show support for Addison and his family.
Coach Ron Rivera said Friday this was "bigger than football" and that the decision on whether Addison played was up to him, noting that this has been an emotional time for the 32-year-old.
Addison on Friday posted a picture on Instagram of him standing next to his brother's coffin with the message, "I love u Geeski. This one F---ed ur Big Bruh up. #LongLiveGeeski."
On Monday, Addison posted on Instagram a picture of him and his brother 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."
Rivera has kept in touch with Addison and provided "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."
Addison ranks 11th in the NFL in sacks this season with 6.5 for a Carolina team that ranks second in the league in sacks with 30, one behind the New England Patriots, who have played one more game.
He learned of his brother's death after the 51-13 loss to the 49ers. The shooting happened at 7:15 p.m. in Birmingham. Police found Rodriqcus and a woman inside a vehicle suffering from gunshot wounds.
Rodriqcus was pronounced dead at the hospital.
Birmingham police on Tuesday reportedly charged 22-year-old Darius Frazier of capital murder for the death of Rodriqcus and attempted murder for the shooting of the woman.