The suspension begins immediately, meaning Johnson will miss Sunday's game against the New Orleans Saints for the NFC South lead. Both teams are 8-3.
Johnson has started all 11 games this season. He has 16 tackles and no sacks. He would be able to return to the active roster on Dec. 25, in time for the team's regular-season finale at Atlanta.
"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, 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."
It is the first suspension for violating the league's PED policy for Johnson.
Coach Ron Rivera said he learned of Johnson's situation on Thursday night and spoke to him about it.
"That's just disappointing,'' Rivera said. "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, who ranks second on the team's all-time sacks list with 67.5, also is subject to a fine of four-seventeenths of his 2017 salary. He re-signed with the Panthers prior to this season on a two-year deal worth $9.5 million. His base salary this year is $1 million.
Julius Peppers, the franchise's career leader with 89.5 sacks, will replace Johnson in the starting lineup opposite Mario Addison. Rookie Bryan Cox Jr., who has played in two games, will be active and join the rotation that also includes Wes Horton.
The Panthers will activate Damiere Byrd from injured reserve to replace Johnson on the 53-man roster. The plan already was to activate Byrd to add more speed at receiver with second-round pick Curtis Samuel out for the year with an ankle injury.
Pro Bowl tight end Greg Olsen returned to practice Friday on a limited basis. Olsen was activated from injured reserve for last week's game against the New York Jets after missing eight games with a broken foot.
He did not play in the second half after experiencing soreness in the foot and did not practice Thursday.
Rivera said he was optimistic about all three, but said how they get through Saturday's walk-through will be key.