The suit, filed by lawyer Max Schrems, claims a symbolic USD 660 per plaintiff from Facebook for several out of a "long list" of alleged violations of the law, his advocacy group Europe-v-Facebook said.
These include its privacy policy, Facebook's alleged participation in the US National Security Agency's PRISM snooping programme, and tracking users' visits to other websites with for example the "Like" function.
Media-savvy Schrems, who first took on Facebook several years ago as a student, filed the legal action in Vienna last week. He had to limit numbers signing on to it to 25,000 after some 7,000 signed up every day.
The suit is directed against Facebook's Ireland-based subsidiary, the US firm's headquarters for its overseas operations, and was not open to users from the United States and Canada. The subsidiary has to abide by EU data protection laws, which are more stringent than those in North America.
The majority of those who signed up were from Europe, with the biggest numbers from Germany, Austria and the Netherlands.