Kyushu Jangara is a Ramen shop which serves a vegan option (1000Yen).
It is a restaurant chain with stores all over Japan. We went to the one in Harajuku, but there are more shops in Ikebukuro, Akihabara, Omotesando ... Check out there website for details: http://kyushujangara.co.jp/shops/
The Ramen had a nice and strong taste and I would definitely recommend it. As it's not all vegan it's especially recommendable if you want to eat out together with someone who likes to eat meat.
1 Chome-13-21 Jingūmae, Shibuya-ku, Tōkyō-to 150-0001