Both incidents have been attributed to neo-Nazis.
“Today's ban is a clear message: Right-wing extremism and antisemitism have no place in our society,” Mr Seehofer said on Thursday.
The interior ministry said Combat 18 Deutschland members were convicted of bringing ammunition into Germany from the Czech Republic after returning from shooting practice.
Police officers raided the homes of Combat 18 Deutschland members in six German states early on Thursday morning, seizing mobile telephones, laptops and pro-Nazi propaganda material.
Its statement said the group “stands in the tradition” of Britain’s Combat 18, a white supremacist stewarding group founded in 1992 by members of the BNP.
It took the numbers in its name from the first and eighth letters of the alphabet — A and H — for Adolf Hitler and soon spread to other countries, including Germany.
The group’s Canadian arm was listed as a terrorist entity in June 2019.
