Speaking after a meeting with European Facebook executives in Berlin, Justice Minister Katarina Barley said the firm's assurances that it had already cracked down on the misuse of personal data were "not enough".
"In future we will clearly have to monitor companies like Facebook more strictly and punish data protection violations severely and quickly," she told reporters.
Facebook was plunged into crisis when a whistleblower revealed that a British consultancy linked to US President Donald Trump's 2016 campaign harvested the data of some 50 million Facebook users without their consent.
The revelation reignited longstanding European concerns that the social media giant was not doing enough to protect the privacy of its users.
The issue is particularly sensitive in Germany, a nation still haunted by the surveillance carried out by the Nazis and the communist-era Stasi secret police.
Barley said Facebook should be more transparent with its users, who should be informed in "clear, precise and simple language" how their personal data will be used, and given the chance to opt out if they object.
She also welcomed new European Union regulations that will take effect in May and will force social media firms to better protect users' online privacy -- or face huge fines.
The British firm at the centre of the controversy, Cambridge Analytica, has been accused of exploiting the hijacked data to create detailed psychological profiles to target potential Trump voters.
The data was obtained via a personality quiz app that was downloaded by some 270,000 people, but also scooped up details about their Facebook friends without their knowledge -- as was possible under Facebook's rules at the time.
Barley said Facebook was still working to determine exactly how many German users were affected by the data breach.
Around one percent of the people who downloaded the quiz were from Europe, the Facebook executives told Barley.
Facebook has faced growing scrutiny in Germany in recent years.
The country's competition watchdog in December slammed the company for using its dominant position to "limitlessly" harvest user data from outside websites and apps, which is then used to create "hyper-targeted" ads.
Germany also has one of the world's toughest laws against online hate speech, which gives firms like Facebook 24 hours to remove posts that violate German legislation or risk fines of up to 50 million euros ($62 million).
Facebook chief Mark Zuckerberg has apologised for the Cambridge Analytica data breach, which he said had betrayed the trust of the website's more than two billion users.
"We're now taking steps to make sure this doesn't happen again," he said in an ad taken out in US and UK newspapers at the weekend.