Arborio rice is not wheat. It really and truly is rice. It is less processed than the usual short grain white rice.
http://culinaryarts.about.com/od/ricegrains/p/arborio.htm "Because it undergoes less milling than ordinary long-grained rice, it retains more of its natural starch content. Cooking releases this starch, giving risotto its creamy consistency. A pound of arborio rice can absorb up to 6 cups of liquid without becoming mushy."
It is possible to find brown arborio rice, and it is possible to make risotto with regular short grain brown rice. You results may not be quite as good as a good arborio rice, however.