Anne Sinclair, Strauss-Kahn's wife of two decades and once a diva of French journalism, was stoic last year as he faced allegations by a New York hotel maid of sexual assault. The charges were dropped but he faces a civil lawsuit in that case and is being investigated in France for suspected links to an alleged prostitution ring.
Closer said Sinclair had asked Strauss-Kahn to leave a month ago. It cited no sources.
A statement Friday by Henri Leclerc and two other attorneys said the couple "decided to file suit against this publication for invasion of privacy." It made no mention of a separation.