The suit accuses the company of disseminating copies of Tarantino's unproduced screenplay, "The Hateful Eight," by offering readers a link to another website where the script was posted.
Tarantino told Deadline.com last week he planned to make the western his next project, then decided not to shoot the movie after someone made copies of the script and distributed it through Hollywood.
He said he believes one of the six people he trusted with the script had let someone else see it.
After the story of the leak broke, Gawker's Defamer website posted a link to the 146-page script under the heading, "Here Is the Leaked Quentin Tarantino Hateful Eight Script."
"Gawker Media has made a business of predatory journalism, violating people's rights to make a buck," the Hollywood Reporter quoted Tarantino's lawsuit as saying. "This time, they went too far. Rather than merely publishing a news story reporting that plaintiff's screenplay may have been circulating in Hollywood without his permission, Gawker Media crossed the journalistic line by promoting itself to the public as the first source to read the entire screenplay illegally."
Gawker editor John Cook said on the website Monday "contributory infringement is a legal theory that has traditionally been deployed against file-sharing sites and search engines -- venues that explicitly exist as directories to copyrighted content. Gawker and Defamer are news sites, and our publication of the link was clearly connected to our goal of informing readers about things they care about. As far as I can tell [but I'm no lawyer!], no claim of contributory infringement has prevailed in the U.S. over a news story. We'll be fighting this one."
He further emphasized Gawker did not initially leak the script or encourage others to do so, but merely told its readers where to find it after the Oscar-winning filmmaker "turned his script into a news story, one that garnered him a great deal of attention."
Tarantino's films include "Reservoir Dogs," "Pulp Fiction," "Kill Bill," "Jackie Brown," "Inglourious Basterds" and "Django Unchained."
Notable deaths of 2014 [PHOTOS]