I asked all around town, and finally found this place... as far as I can tell, this is the only 100% vegetarian place in town. The location is in the north part of the city.
They are open continuously from 830am to 800pm, but it's really only a place for snacks, not full meals. They have bread, cookies, products made from soy, juices, yogurt, dehydrated fruit, etc. For a meal, you can combine items such as veggie sandwiches, soup, oatmeal, arepas, tamales and whatever else they may have that day. On Fridays after 330pm and on Saturday, they have Super Arepas (sounds great, but I couldn't stay in town long enough to sample them!). The day I went, I tried one of the veggie tamales and a juice... both were very good.
If for some reason you find yourself in Monteria, please stop by and support this business!
Cons: Location not in tourist area