There is no evidence that they did. Even the general image of a 'levy' or a 'popular army' (that is, the general population taking up arms) is dubious.

Now, during the Cimbric Wars in the 2nd century BC (600 years before), at a Roman fight against a migratory group in Southern France (just to give an idea of how far removed this is from 400 ad northern germany) there are descriptions of the women committing collective suicide and killing children to avoid getting captured. We also have later references to women cheering at the sidelines, so to say, at armies fighting.

The other reference to women fighting is from the other side of the 'dark ages', when we have legends written down in 12th century Iceland that speak of individual heroic women taking up martial duties in absence of a suitable male family member. However, 1. it is unclear to what extent this is 'artistic licence' from the author (similar to Greek Amazons, or Valkyries), 2. this happens only in aristocratic cases, similar to having queens despite a generally patriarchic society, and 3. this is at the end of the Viking age in Scandinavia, not 4th century northern Germany.

There are a few graves from the period that have 'weapons' together with a skeleton that is biologically determined to be likely female. However, there are a few issues here. Biological sex determination of fragmentary human remains is not particularly accurate (these 'women' might just be men with a feminin build, so to say). Also, we need to define when a knife becomes a weapon, or when it is just a tool. Thirdly, and most importantly, there is not a 1:1 relation between having weapons in the grave and being a warrior in life. Again, it is likely that the weapons signify a status in society (being a member of the arms-bearing class) rather than being someone who actually fights. If we compare this rather circumstantial and dubious evidence for women warriors in the graves, with the ubiquity of weapons in male graves (over 50% in many societies of the period), I think we can safely say that warfare was an exclusively male affair. However, many societies at that time practiced cremation with little grave goods, so that does complicate the picture a bit.

Now, this does not mean that women never fought. Women, also in this period, are primarily the custodians of the home, so it is still possible that a woman can defend herself when physically attacked (just as in any society, really). But them being warriors, or included in a levy, is very unlikely.