"Right-wing extremism and anti-Semitism have no place in our society," Germany's Interior Ministry said, the BBC reported on Thursday.
Combat 18 takes its name from the Nazi dictator Adolf Hitler's initials, referencing the first and eighth letters of the alphabet.
The group originated in the UK in the 1990s but spread to other countries.
On Thursday, more than 200 police officers searched several properties belonging to leading members across six German states, Interior Minister Horst Seehofer said in a statement.
According to the ministry, the decision was made following the murder last June of pro-migrant German politician Walter Lubcke, and the deadly attack months later on a synagogue in the eastern city of Halle.
"The hideous murder of district president Dr Walter Lubcke and... the terrorist act in Halle last year have shown us, brutally, that right-wing extremism and anti-Semitism are a significant danger to our free society," the minister said.
Items recovered during the raids, which took place in the early hours of Thursday, included mobile phones, laptops, clothing, Nazi memorabilia and propaganda materials, the statement added.
The ministry added that, separate to the incidents mentioned by Seehofer, the purpose of Combat 18 and its activities contravened Germany's constitutional law and order.
Neo-Nazi groups are already outlawed in many European countries.
Last February, French President Emmanuel Macron said his government would act to dissolve Combat 18 and other extreme-right groups, which he said had fuelled hatred and promoted discrimination.
The move followed a series of high-profile anti-Semitic attacks in France.
The crackdown in Germany comes on the day that world leaders meet in Jerusalem to mark the 75th anniversary of the liberation of the Auschwitz death camp in Nazi-occupied Poland.
Combat 18 is still believed to have a small presence in the UK. Suspected members of the group have for years been banned from joining the police and prison services.
( With inputs from IANS )