Said that, there's a nice vegetarian Ramen shop in Tokyo Station:
That said, getting a really good umami flavor and rich texture in a vegan broth is hard - not impossible, but much harder than with meat. And frankly, most vegetarians are lousy cooks who don't pay attention to good textures and flavors, and most meat eaters are lazy cooks who don't learn how to get richness without meat doing the heavy lifting for them.
For vegetarian/vegan, a kombu-based broth can get that richness, but it'll take a lot of patience to make (this is also true of bone-based meat broth).
On the other hand, I'd love if they didn't put fish stock in everything, including ramen, I really like ramen. I found a ramen house where I live (Sao Paulo, there's a huge Japanese/Asian neighbourhood in here, and it's a great place to find vegetarian ingredients such as mushrooms) which offers one dish without fish stock, but they closed and reopened, and now I'm not sure they still have it on the menu.
And what has been said about vegetarianism in Japanese culture is true. They probably think fishes come from trees. I actually had an uncle (I'm from a Japanese family) who said he was vegetarian but ate fish.
I explained this to the ramen shop proprietor. He came out with a bowl of ramen with chashu (pork) on top of it. When I pointed out that pork does in fact count as a meat product, he plucked it off with chopsticks. I then said "Excuse me, I don't mean to be a bother about this, but I can't help but notice that you poured the broth from a pan marked Pig. Is there, I don't know, pork in the broth?" "Oh you read Japanese!" "Yep, literacy is a handy quality in a translator." "Do your guests read Japanese?" "No." "Then as far as they know it's hearty vegetable broth now isn't it!"
It's a brilliant, simple dish -- and typical for Japanese cuisine it can be magnificent in its simplicity if you are careful when selecting what to put in.
I would personally prefer some beef, fish, shell fish ... but there's nothing really inherent in the dish that dictates one need it. You'll need to amass things that in aggregate makes for a good broth -- and vegetables certainly can do that.
[ed: Ah, I was a bit quick googling. The recipe is great for the first part of the nabe -- but it doesn't mention that one way to end the whole thing, is, when all the other ingredients have been eaten, and have left their taste in the broth: Add ramen - and eat with the broth.]
[1] http://www.thekitchn.com/cooking-japanese-nabemono-106649
It's called Yamadaya.