While many types of hate speech and online toxicity have been the focus of extensive research in NLP, toxic language stigmatizing poor people has been mostly disregarded. Yet, aporophobia, a social bias against the poor, is a common phenomenon online, which can be psychologically damaging as well as hindering poverty reduction policy measures. We demonstrate that aporophobic attitudes are indeed present in social media and argue that the existing NLP datasets and models are inadequate to effectively address this problem. Efforts toward designing specialized resources and novel socio-technical mechanisms for confronting aporophobia are needed.