Interior Minister Hans-Peter Friedrich banned one particular network, known as "Millatu Ibrahim", for "working to undermine Germany's constitutional order."
Authorities are also investigating two other networks, called Dawa FFM and "The True Religion", with a view to a possible ban.
According to documents seen by AFP, the interior ministry decided to ban Millatu Ibrahim, based in the western town of Solingen, after an explosive vest was found during a search of premises in Berlin last month.
"The vest is a further sign of the organisation's underlying aggression," the papers said.
The ministry said an inflammatory speech by one of the network's preachers helped spark violent clashes between the Salafist community and police in Solingen on May 1.
It had also found audio and video messages in which the group proclaimed war against democracy and threatened "unbelievers".
Around 850 police raided more than 70 different premises in seven different regional states, targeting flats, mosques, schools and local associations. The biggest operations took place in the states of North Rhine-Westphalia and Hesse, the ministry said.
Laptops and mobile phones, as well as video equipment and material were seized and were currently being analysed, Friedrich said.
"I believe this shows that a constitutional democracy is capable of responding to those who want to eliminate freedom and democracy," the minister said.
"We are ready to defend freedom and fundamental rights in this country and I hope this is understood by those who are of a different opinion," he said.
In a statement, the regional state interior minister of North Rhine-Westphalia, Ralf Jaeger, described the police operation as a "decisive step by the security services in the fight against dangerous extremists."
"Today's operation shows that we're turning up the pressure on the Salafists," Jaeger said.
At the beginning of May, German authorities opened a probe against 44 members of the Salafist community and 37 others after violent clashes with police in Solingen.
The Salafists have raised concern with their drive to convert non-Muslims, a campaign that has involved handing out 25 million copies of the Holy Quran in Germany, Austria and Switzerland.
Authorities estimate there are about 2,500 Salafists in Germany.
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