The group, called The True Religion (Die wahre Religion), is now also banned, Interior Minister Thomas de Maiziere said. German officials consider the group to be unconstitutional and against the principle of having understanding among different nations, according to DPA information.
"Under the pretext of promoting Islam, under the pretext of supposedly harmless distribution of translated versions of the Koran that took place in pedestrian zones, hate messages were propagated and young people radicalized," added the interior minister.
The organization's controversial programme called "Lies!" distributes copies of the Koran in German. But experts say the translation is a particularly strict version from the original Arabic text.
Germany's domestic security agency BfV accuses group members of being sympathizers with armed jihad and terror attacks, claiming they had built up a nationwide recruitment network and reserve of jihadists.
Tuesday's ban is the biggest such prohibition in Germany targeting Islamist groups after another organisation called "The Caliphate State" was outlawed in 2001.
De Maiziere stressed that Tuesday's action is not targeted against the general distribution of translated Korans, but against those who "abuse religion and who use it as a pretext to spread extremist ideology and to back terrorist organisations".
"The 140 departures by the group's activists speak for themselves," the minister said.
"By banning this organisation, a major source of radicalization has been eradicated nationwide. Those who spread hate messages can't hide behind freedom of religion, the Interior Ministry has underlined this with the ban today," he added.
The BfV estimates that the number of radical Islamists in Germany totaled about 9,200 as of the end of October and continues to rise. The number of potential Islamist terrorists is estimated to be 1,200.