Local authorities said more than 25,000 private photos and pieces of personal information from the Kaunas-based Grozio Chirurgija clinic were published on the internet.
The leak includes intimate photos and data of more than 1,500 Brits, MailOnline has learned.
A hacking group called Tsar Team, who broke into its servers earlier this year, is now demanding ransom from clients in Germany, Denmark, Norway, the UK and other EU countries.
Staikunas said victims were asked to pay up to 2,000 euros (£1,740) to guarantee that nude images, passport copies, social security numbers and other data would not be shared publicly.
The hackers also demanded the clinic itself pay 344,000 euros (£299,000) to prevent the data dumping, but it refused.
The clinic warned clients not to open or download anything suspicious believed to have been sent by the blackmailers, and to forward any correspondence to cops.