The BKA said in a statement that Facebook's terms and conditions aren't clear enough for users to grasp how much control over their data they are agreeing to give it.
"Market dominant companies have special duties, including appropriate contractual conditions," BKA President Andreas Mundt said. "For internet services financed by advertizing, such as Facebook, users' data have a particular significance."
It's the latest in a series of run-ins for Mark Zuckerberg's social network in Europe's largest market. On Monday, a Berlin court imposed a fine of €100,000 ($109,000) for failing to react quickly enough to an order to change its terms and conditions to bring it into line with German copyright law. The offending clause, which the company has now changed, was related to Facebook's rights to use material uploaded by users.
More controversially, Facebook is embroiled in a running controversy over the spread of hate speech on its network which has mushroomed against the background of the migrant crisis.
Hamburg prosecutors closed one criminal investigation into the managers of Facebook's German subsidiary after concluding that they were only responsible for generating advertizing business rather than for the site's content. But another investigation into the potential liability of Martin Ott, managing director for northern, central and eastern Europe, is still ongoing. The investigation may lead to charges of being an accessory to inciting racial hatred.
German law only allows natural persons, rather than companies, to be the subject of criminal charges. But Facebook's structure makes it difficult to pin responsibility for the site's content on any locally-based employees. However, Würzburg-based lawyers Chan-jo Jun and Christian Solmecke earlier this month filed a criminal complaint against Zuckerberg himself, saying "it's necessary to widen the action to (Facebook's) international companies and their managers."
A spokeswoman for the Hamburg prosecutors told Fortune that they are still examining the merit of that complaint.
Jun and Solmecke alone claim to have collected over 300 instances of hate speech that the network hasn't taken down, almost always with the defense that the posts don't violate its community standards.
Facebook says it is conforming with German law and that it has upped its efforts to take down hate speech. Facebook didn't immediately reply to a request for comment Tuesday.