Here are the ingredients (from http://www.bk.com/Food/Nutrition/ingredients.aspx
BK VEGGIE® BURGER
Vegetables (Mushrooms, Water Chestnuts, Onions, Carrots, Green Bell Peppers, Red Bell Peppers, Black Olives), Textured Vegetable Protein (Soy Protein Concentrate, Wheat Gluten, Water for Hydration), Egg Whites, Cooked Brown Rice (Water, Brown Rice), Rolled Oats, Corn Oil, Calcium Caseinate, Soy Sauce (Water, Soybeans, Salt, Wheat), Onion Powder, Corn Starch, Salt, Hydrolyzed Corn, Soy, and Wheat Protein, Yeast Extract, Natural Flavors from non-meat sources, Sugar, Soy Protein Isolate, Spices, Garlic Powder, Dextrose, Jalapeño Pepper Powder, Celery Extract. Contains: Soy, Wheat, Milk and Egg. This is NOT a vegan product.
So that's a 'no' then, if you don't want any animal products