The Australian Competition and Consumer Commission (ACCC) has commenced proceedings against Facebook and a pair of its subsidaries at the Federal Court of Australia, alleging the companies engaged in "false, misleading, or deceptive conduct" when promoting the Onavo Protect VPN app.
The ACCC points to ads at the time that said data would be kept "secret" and "safe".
The watchdog said it was seeking declarations and pecuniary penalties in bringing the action.
Onavo was purchased by Facebook in 2013.
Last week, Facebook suspended accounts linked to Vietnamese hacking group APT32.
A day earlier, the US Federal Trade Commission and a bipartisan coalition of over 40 state attorneys-general filed anti-trust suits against Facebook.
The FTC said in its lawsuit that Facebook initially tried to compete with Instagram on the merits by improving its own offerings, but it ultimately chose to buy Instagram to neutralise the direct threat posed by Instagram and make it more difficult for another personal social networking competitor to gain scale.
The lawsuits also allege companies that rebuffed offers to be acquired by Facebook -- or those that posed a competitive threat -- would subsequently be cut off from access to various key components within the social networking giant's network.
"For nearly a decade, Facebook has used its dominance and monopoly power to crush smaller rivals and snuff out competition, all at the expense of everyday users," New York Attorney-General Letitia James said.
"Almost every state in this nation has joined this bipartisan lawsuit because Facebook's efforts to dominate the market were as illegal as they were harmful. Today's suit should send a clear message to Facebook and every other company that any efforts to stifle competition, reduce innovation, or cut privacy protections will be met with the full force of our offices."