§ Section 1 of the German Weapons Act states whether swords are weapons:
§ Section 1 Subject matter and purpose of the Act, definitions
(1) This Act regulates the handling of weapons or ammunition, taking into account the interests of public safety and order.
(2) Weapons are
1. firearms or equivalent objects and
2. portable objects,
a) which by their nature are intended to eliminate or reduce the ability of people to attack or defend themselves, in particular blunt weapons;
b) which, without being intended for this purpose, are suitable, in particular due to their nature, handling or mode of action, for eliminating or reducing the ability of humans to attack or defend themselves, and which are specified in this Act.
(3) Anyone who acquires, possesses, transfers, carries, transfers, takes, shoots, manufactures, processes, repairs or trades in a weapon or ammunition is deemed to be handling it.
(4) The definitions of weapons and ammunition and the categorisation of objects under subsection (2) no. 2 letter b as weapons, the definitions of types of handling and other legal terms relating to weapons are set out in more detail in Annex 1 (Definitions) to this Act.
Source: https://www.gesetze-im-internet.de/waffg_2002/index.html#BJNR397010002BJNE000010301
The Annex 1 mentioned in the text: https://www.gesetze-im-internet.de/waffg_2002/anlage_1.html
According to our interpretation, samurai swords fall under the Weapons Act and are therefore regulated by the Weapons Act. What the situation is for purely decorative swords is in this article illuminated.
A few explanatory words:
Please note that this is in no way legal advice, a recommendation for action or similar!
The most important legal regulations in this context: