The Hamburg Commissioner for Data Protection and Freedom of Information said that the social network had not obtained effective approval from WhatsApp's 35 million German users.
Facebook bought WhatsApp for $19bn (£14.6bn) in 2014 as a way to reach out to a younger audience.
It is to appeal against the order.
"We will work with the Hamburg DPA in an effort to address their questions and resolve any concerns," it said in a statement.
The data watchdog said that Facebook and WhatsApp were independent companies and should process their users' data as such.