Johnson will begin his suspension immediately and miss Sunday's key NFL South battle against the New Orleans Saints, who are tied with the Panthers at 8-3.
Johnson will be eligible to return to the Panthers' active roster on Dec. 25 and available to play in the final regular-season game against the Atlanta Falcons on Dec. 31. He started all 11 games this season, making 16 tackles and no sacks.
"I accept full responsibility," Johnson said in a statement released by the team. "I have been recovering from back surgery, dealing with the daily grind of football and mistakenly thought this could help. It was an error in judgment on my part.
"We have a special group here I wanted to be a part of and felt an obligation to do my part by getting back as soon as possible. I have always prided myself on being a person who does things the right way, through hard work, dedication and sacrifice. I want to apologize to my team, (owner) Mr. (Jerry) Richardson and Panthers fans for this mistake. Regretfully, I have disappointed people, but I promise to come back ready to redeem myself when this suspension is over."
The 31-year-old Johnson re-signed with the Panthers prior to this season on a two-year deal worth $9.5 million. He has 67.5 career sacks, second on the team's all-time list.
Coach Ron Rivera told reporters after Friday's practice that he learned of Johnson's situation on Thursday night.
"That's just disappointing," Rivera said of Johnson's suspension for the team's stretch run. "It's hard. The biggest thing we've all got to understand is it's no different than if a guy blew an ankle out and you've got to have the next man ready to roll."
Johnson will be replaced in the starting lineup by 37-year-old Julius Peppers, the franchise's all-time leader with 89.5 sacks, including 8.5 this season. Peppers has 152 NFL sacks during his 16-year career.
The Panthers will activate wide receiver Damiere Byrd from injured reserve to take Johnson's spot on the 53-man roster.
Byrd suffered a broken left arm against the New England Patriots in Week 4.