As per People for the Ethical Treatment of Animals, also known as PETA, almost every bread product is suitable for vegans. Wheat bread is traditionally made with plant-based ingredients, which include whole wheat. However, some forms of bread items can be non-vegan, like honey wheat bread for instance. Honey is generally regarded as a non-vegan ingredient. That said, a minority of vegans also considers it a product suitable for them.
 
Vegans are supposed to not eat anything that comes as a result of animal exploitation. Humans take advantage of bees to procure honey from their hives. This makes honey a non-vegan product, and the same goes for any product made with it. So, just be sure to look at the list of ingredients when shopping for wheat bread. If honey is in the product, then you might want to reconsider purchasing it.