Cosby's lawsuit says Johnson joined other women making accusations against him to revive her waning career and to help sell copies of her memoir.
The lawsuit alleges defamation and intentional infliction of emotional distress, saying Cosby and Johnson never spent any time alone in his house, he never drugged her and "her story is a lie."
"I am aware of the statements from Bill Cosby," Johnson said in a statement. "In cases of rape and abuse, abusers will do whatever they can to intimidate and weaken their victims to force them to stop fighting. I ask for your support of all of the victims involved."
More than 40 women have come forward
to publicly accuse Cosby, 78, of assaulting them over four decades, usually saying he drugged them first. No criminal charges have been filed against Cosby.
Last week, Cosby filed a countersuit against seven other women
who accused him of sexual assault and sued him for defamation. Cosby said the women's accusations hurt his reputation so much that plans for a new family comedy on NBC were derailed.
She said that in the mid-1980s, she went to Cosby's residence to work on acting exercises, including one in which she acted drunk, when Cosby asked her to have a drink from his cappuccino machine.
"I knew by the second sip of the drink Cosby had given me that I'd been drugged -- and drugged good," she wrote. Johnson said she struggled so much that Cosby took her out of the house and put her into a cab.
Johnson later talked about the alleged incident to other publications and television shows such as "The View," "Nightline" and "Good Morning America." She devoted a chapter to it in her 2015 autobiography, "The Face That Changed It All."
In a press release, Cosby lawyer Monique Pressley called Johnson's statements "an opportunistic attempt to resuscitate her own career and benefit herself financially from the wave of media attention surrounding her false allegations against Mr. Cosby. ..."
Cosby seeks unspecified damages, an injunction requiring Johnson to retract her statements, removal of the chapter about Cosby in future copies of her memoir and removal of the chapter from unsold copies.
Pressley filed the lawsuit in Los Angeles County Superior Court.
In another action, Cobsy's lawyers filed a motion to dismiss a lawsuit filed last October by Renita Hill, one of his accusers.
Hill appeared in the "Picture Pages" educational videos with Cosby in the 1980s when she was a teenager.
She said Cosby sexually abused her from 1983-87 and paid for her college education until she decided to have no more contact with him. She filed for defamation after Cosby, his lawyer and his wife said in the media that her accusations were not true.
The Cosby motion says Hill's complaint doesn't meet the bar for defamation and notes that the three media comments mention Hill by name.
Hill's lawsuit is in the U.S. District Court of western Pennsylvania.