The interior ministry said the organisation that it banned, Muslim Interaktiv, represented a threat to the country's constitutional order by promoting anti-Semitism and discrimination against women and sexual minorities.
The group is known for a savvy online presence used to appeal especially to young Muslims who may feel alienated or discriminated against in Germany's Christian majority society.
The German government argued the group was a particular threat because it promoted Islam as the sole model for the social order and maintained that Islamic law should take precedence over German law in regulating life in the Muslim community, including in areas such as the treatment of women.
The German government has in recent years been acting more forcefully against extremism, and banned several extremist groups, including several far-right and Muslim organisations.
The crackdown comes after a spate of attacks, both by Muslim extremists and far-right groups plotting to overturn the country's order.
"We will respond with the full force of the law to anyone who aggressively calls for a caliphate on our streets, incites hatred against the state of Israel and Jews in an intolerable manner, and despises the rights of women and minorities," German Interior Minister Alexander Dobrindt said.
The ministry also announced that investigations were under way against two other Muslim groups, Generation Islam and Reality Islam.
"We will not allow organisations such as Muslim Interaktiv to undermine our free society with their hatred, despise our democracy, and attack our country from within," the minister said.
The ministry said the group "is particularly opposed to gender equality and freedom of sexual orientation and gender identity".
"This expresses an intolerance that is incompatible with democracy and human rights."
Authorities on Wednesday searched seven premises in the northern city of Hamburg, and also conducted searches in 12 premises in Berlin and the central German state of Hesse in connection with the other two groups under investigation.
The government said Muslim Interaktiv sought to indoctrinate as many people as possible and "thus create permanent enemies of the constitution in order to continuously undermine the constitutional order".
In a recent report, the domestic intelligence service of Hamburg wrote that in their online posts and videos, the leaders of Muslim Interaktiv addressed socially relevant topics in order to exploit them "to portray a supposedly ongoing attitude of rejection by politics and society in Germany towards the entire Muslim community", DPA reported.
