Court documents filed in Los Angeles Superior Court state that the article, posted online on October 18, included false and defamatory claims that the actor had cheated on his wife with tennis pro Edit Pakay, 28.
"This is false. It never happened," the suit states.
The tabloid is claimed to have run the story despite being told "point blank" that it was false and that the pro was "explicitly and specifically denying a romantic or sexual relationship with David Duchovny".
Duchovny, who recently confirmed his separation from Leoni, is seeking $1 million (£612,000) in damages for defamation and invasion of privacy.