The lawsuit, filed in US District Court in Los Angeles by a man identified as John Doe, seeks class-action status.
The lawsuit accuses Ashley Madison and parent company Avid Life Media Inc, which is based in Toronto, of negligence and invasion of privacy, as well as causing emotional distress.
The lawsuit seeks unspecified damages.
The lawsuit follows a breach of the Ashley Madison website by a group called the Impact Team, which downloaded "highly sensitive personal, financial, and identifying information of the website's some 37 million users," the lawsuit said.
The hacker group threatened to release information if the site was not shut down, and in August, when the site had not been shut down, published "stolen personal information," the suit said.
The data, which was dumped online, included millions of email addresses for US government officials, UK civil servants and high-level executives at European and North America corporations.
The lawsuit claims that the data breach could have been prevented if the company had taken "necessary and reasonable precautions to protect its users' information, by, for example, encrypting the data."
The lawsuit says that in addition to making "extremely personal and embarrassing information ... accessible to the public," the data breach made personal details such as addresses, phone numbers and credit card information available on the web.
Avid Life Media could not be reached immediately for a comment outside regular business hours.
Avid Life Media was sued in Canada last week in a class-action suit that seeks some $760 million (roughly Rs. 5,050 crores) in damages.
The case is filed in the US District Court, Central District of California No. 15-cv-06405.
© Thomson Reuters 2015