The 48-year-old actor said he did so voluntarily, in a statement released Thursday by his lawyer, Stanton Stein. He added: "I ask for respect and privacy for my wife and children as we deal with this situation as a family."
Duchovny's publicist, Flo Grace, confirmed the report, which first appeared on the Web site People.com. She and Stein both declined further comment.
"All of us at Showtime wish David and his family the best during this very private time," the network said in a statement.
The second season of "Californication" begins Sept. 28.
Duchovny starred as the conspiracy-minded Fox Mulder on "The X-Files" TV series and in two films. "The X-Files: I Want to Believe" opened in theaters earlier this summer.
He and his wife, actress Tea Leoni, have two children. The couple married in 1997.