In an internal letter obtained by Der Spiegel, the minister, Ilse Aigner, a long-time critic of the privacy policies at the social networking site, had outlined her objections to the other ministers.
"After an intensive legal review, I have concluded that it is crucial to ensure that the Facebook button is not used on any of our official government websites," she wrote in the letter.
Aigner, who said she quit Facebook a year ago protesting its data security practices, added that "fan pages" which users can join to get information about organizations should also be avoided "in light of justified legal doubts."
In the letter, she said ministries and members of parliament should "set a good example and give data protection its due."
German data protection authorities have raised the alarm in recent weeks over Facebook, and in particular its "Like" button with which users indicate their preferences as they navigate the site.
Privacy watchdogs say the information is collected with the aim of creating detailed user profiles, for example for advertisers.
Facebook said Thursday it would sign up to a voluntary code of conduct in Germany to protect users' data, the first time the site has agreed to such measures in a country particularly sensitive about privacy.